Unit 2: Blog Summary

In this unit, I learned about 7 additional key concepts in physics...

1.) Newton's Second Law

2.) Newton's Second Law Lab (A lab we did to test the law!)

3.)  Free Fall- Falling Straight Down

4.) Falling Through the Air (With air resistance-Sky Diving)

5.) Throwing Things Straight Up (Free Fall)

6.) Falling at an angle (Free Fall)

7.) Throwing Things Up at an Angle (Free Fall)

Just like in the last unit, in each of these concepts, I learned numerous formulas, concepts, and everyday applications. However, what was different was that the concepts became increasingly complicated in knowing which formula to use and when. In addition to explain why exactly a certain reaction occurs. In order to avoid the unnecessary complication, I will break it down for you.

Part One: Newton's Second Law 

1.) What is Newton's Second Law?

     In word form, the answer is Force is directly proportional to acceleration, mass is inversely proportional to acceleration. In symbols that would be written as a=f/m. 

2.) What is the relationship between f (force) and a (acceleration)?

      They are directly proportional meaning if one increases, then the other increases. If one decreases then so does the other. In symbol form that would be written as....

3.) What is the relationship between m (mass) and a (acceleration)?

     They are inversely proportional. If something is inversely proportional with something else that means that as one increases the other would decrease.

4.) What is the formal to find the f weight of an object?

   The formula is written as w=mg.  In word form, this translates to mean force weight=(mass)(gravity).

Examples and Practice Problems 

1.) Imagine a friend is moving out of their apartment! You both see a box already packed up, so you both head for the box. You push on the left with 40N and your friend pushes on the right with 20N. The box has a mass of 10kg. What is the acceleration of the box?

The formula we need to use is a=f/m. Now that we've chosen the correct formula we can begin step one.

Step one: subtract the 20N your friend pushed with from the 40N you pushed with.

- 40N-20N= 20N

Step two: (20N) /  (10kg) = 2 m/s^2

The answer is 2m/s^2!

2.) You are a mover on the second floor of a mansion. You need to get a piano to the second floor, but the door is too small, so you use the window. You hook up a pulley system, attach the piano, and begin to pull.  If the piano has a mass of 15kg and has an upward force of a pulley of 40N and a downward force of only its weight, what is the acceleration of the box?

The formulas we will need are w=mg and a=f/m. We need these formulas because we don't know the total force on the piano just yet. To figure that out we need to use w=mg, then subtract that from the 40N of force we already know is applied on the piano. Then we can divide that by the mass and get the acceleration.

Step One: w=mg

w= (15kg)(10N) <--- (The 10 can from the amount of gravity that is applied on all free falling objects without taking air resistance into account).

w= 150N

Step Two: a= f/m

a= (150N-40N) /  (5kg)

a = (110N) / (5kg)

a= 22m/s^2


3.) If something has a mass of 2kg, what is its weight?

   Step one= w=mg
 
    w= (2kg)(10N)

    w= 20N


4.) If something has a weight of 20N, what is its mass?

    Step one: w=mg

     20N= (m)(10)

     Step two: (20N) / (10) = m

     m= 2kg !

Part Two: Newton's Second Law Lab 

 In this lab we learned how acceleration depends on force and mass! Before beginning we had to answer the following questions...

Pre-lab

1.) What will apply the force that causes acceleration?

The hanging weight

2.) How will you calculate the force?

First, we will need to use w=mg. After, we will use a=f/m.

3.) If the net force on a body is zero, what is the acceleration of that body?

  The acceleration is zero because force and acceleration are proportional.

4.) When the net force on a body is constant, what should the acceleration of that body be?

The acceleration of that body should be constant because force and acceleration are proportional.

Lab- Part A 

After answering those we could get started! The first step was to figure out the mass of the cart and the hanging weight (kg). Using a scale we figured out the having weight's weight was .0497 kg and the cart was 0.4886 kg.  Then we had to use the formula w=mg to calculate the weight of the hanger (N). The answer was .48706. After running a few trials we answered the following questions...

1.) As the mass of the cart was increased, what happened to the acceleration?

    The acceleration decreased

2.) What remained constant in the experiment?

The force

3.) What part of the system exerted the force that caused the acceleration?

The hanging weight.

Now when we entered this all in excel, we had to use the equation of a line.

1.) What is the equation of a line?

y=mx+b

2.) If we assume the y intercept is zero (the b symbol) What do the other parts of the equation of a line stand for from the Newton's Second Law equation?

On the y axis we would graph the acceleration. The slope (m) would be representative of force, which we kept constant. Finally, on the x axis we would graph the mass.

3.) What would the equation of a line look like with the replacements of Newton's Second Law?

(a)= (f)(1/m)

4.) What equation does (a)=(f)(1/m) look like, from a concept in the previous unit?

   a= 1/2(g)(t)

Lab- Part B 

In this portion of the overall lab, we again asked how the acceleration changes. However, in part B the mass is constant throughout the experiment and we just increase the force. To begin the lab we were asked the following questions...

Pre-lab (Part B)

1.) What do you need to find the masses of in order to know the total mass of the system?

    The mass of the cart, hanging weight, and an additional weight

2.) What do you need to do to find the force of the system?

    You need the weight of the hanging weight and the added weight. Then we will use the formula, w=mg.

During the lab

1.) What happened to the acceleration as the force of the cart increased?

      The acceleration increased because acceleration and force are proportional.

2.) What remained constant during the experiment?

      The mass remained constant because we didn't remove the weight, we just moved it from what was being pulled to what was pulling the cart (the force).


 Analysis 

1.) Now assume the y intercept is zero, what could the other parts of the equation of a line stand for form the Newton's Second Law equation?

The acceleration will be on the y axis. The mass is what we kept constant and is what will represent the slope. Finally, the force will go on the x axis.


Post Lab- Questions

1.) If you add mass from the cart to the mass hanger, what will happen to the acceleration of the system? Why?

The acceleration will decrease because the mass and acceleration are inversely proportional.

2.) If you move the mass from the cart to the mass hanger, what will happen to the acceleration of the system? Why?

The acceleration will increase because the force was increased. Force and acceleration are proportional.

3.) Why did we move the mass from the cart to the hanger, instead of just adding mass to the mass hanger

We moved it because otherwise the force would've remain constant.

Why were we able to add mass to the cart when testing the effects of mass acceleration instead of having to move the mass from the weight to the cart?

This is because we were testing different things. The first time we were testing the effects of mass on acceleration. The second time were testing the effects of force on acceleration.

4.) How is Newton's Law different form the definition of acceleration.

      Acceleration is the change in speed. Newton's second law is the net forced divided by the mass which equals the acceleration.


Free Fall- Falling Straight Down

1.) What is free fall?

    When objects fall due to the acceleration of gravity only! There are not affecting by air resistance and the weight of the object doesn't matter.

2.) What is the acceleration of a falling object?
 
     The acceleration of all falling objects will be 10m/s^2.

3.) What formula you use to find out the distance of a free falling object? (How high)

      The formula to use is d=1/2(g)(t^2). In words, this translates to distance equals half of the acceleration due to gravity (10 m/s^2) multiplied by the squared time (t^2).

4.) What formula do you use to find the velocity of a free falling object? (How fast)

     The formula you use is v=gt. In words, this translates to velocity equals the acceleration due to the force of gravity (10m/s^2) multiplied the time.

Examples and Practice Problems 

1.) An avalanche is coming! You are at the edge of the cliff and have to jump, but you want to know if you have a chance of surviving the fall. You take a puff ball of of your helmet and drop it off of the edge of a cliff. The ball falls for 8 seconds. Since the ball started from rest, how high was the cliff. How fast was the ball moving when it hit the ground?

To figure out the height of the cliff we have to use the formula d=(g)(t^2).

Step one: d=1/2(g)(t^2)

d= 1/2 (10)(8^2)

d= 1/2 (10) (64)

d= 1/2 (640)

d= 320 meters

Now we need to figure out how fast the ball was moving when it hit the ground.  To do this, we will need the formula v=gt.

Step one: v=gt

v= (10)(8)

v= 80 m/s

2.) For this next problem we are going to take the same situation, but in this case we do not know the time. We want to know how the far the ball will have fallen after 5 seconds? In addition to, how fast will a ball be going after 5 seconds.

To figure out how fat the ball has fallen after 5 seconds, we need to use the formula d=1/2(g)(t^2).

Step one:

d= 1/2(g)(t^2)

d= 1/2 (10)(5^2)

d= 1/2 (10)(25)

d= 1/2 (250)

d= 125 m (meters)

To figure out how fast the ball is going after 5 seconds, we need to use the formula v=gt.

Step one: v=gt

v= (10)(5)

v= 50 m/s


Falling Through the Air (With air resistance-Sky Diving)

For this section, refer to the worksheet posted below to figure out the answers. I will mark the ones the questions you need to use the worksheet for by saying, " Refer to worksheet" in bold. However, for some of  the questions I pose, I will explain why it happens.

1.) What is the relationship between velocity and air resistance?

      They are directly proportional. This means that as one increases, the other increases and as one decreases, the other decreases.

2.) what is the relationship between force and acceleration?

You should remember this from a concept I introduced in this blog. If you don't then you haven't learned it. Return to section #1- Newton's Second Law and redo the practice questions. Then return to this question.

3.) What formula do you use to find the net force?

      The formula is f net= f weight- f air.

4.) What do we use to find mass and force when falling through the air?

    To figure this out subtract the f weight from the f air. In formula form, f weight- f air.


5.) What changes when skydiving?

     The net force changes because your speed changes. In other words, the change of one causes the change of the other.

6.) What is terminal velocity?

      Terminal velocity is when you reach equilibrium and are moving at a constant velocity. At this point your velocity is at its highest point. You acceleration and f net are at their lowest points.


7.) At what points are you velocity, acceleration, and f net before you jump out of the plane?

    At the start your velocity is at 0m/s,  your acceleration and F net are at there highest points.

8.) What happened as you fell? Refer to worksheet 

    You speed up because your f air increased. This causes your F net to decrease which causes your acceleration to decrease.

Now imagine you are skydiving, you are falling... 

1.) What happens to the force of air resistance as you fall through the air?

It increases.

2.) Why does this change occur?

It increases because your f air is increasing. Your f air is increasing because your velocity is increasing and f air is proportional to velocity.

3.) What are the two things that affect the amount of the force or air resistance?

     The two things that affect it are the velocity and the surface area. These are directly proportional meaning that as one increases the other will decrease or as one decreases the other decreases.

Now you have reached Terminal Velocity A….

1.) What causes you to reach terminal velocity?

You surface area increasing or your body position changing can cause your air resistance to increase or decrease. This can cause you to reach terminal velocity.

 2.)  At what points are the net force and acceleration at terminal velocity?

They are at their lowest points when they are at terminal velocity. 

     Now your parachute has opened….

1.) What happens to the net force and the acceleration once the parachute opens? Refer to worksheet

As soon as you open in it the surface area increases which causes the acceleration and net force to go in the upward direction. Now in the upward direction, they are both increasing which causes the f air to be larger than the f weight.

2.)  After your parachute opens, what happens to your velocity and why? Refer to worksheet

The velocity is decreasing because acceleration and velocity are going in opposite directions. 

 3.)  As you are falling you eventually reach terminal velocity A. Then you open your parachute and after a little while you reach terminal velocity B. How does terminal velocity A and B compare with each other? Why?

Terminal velocity B is slower because acceleration and velocity are going in opposite directions. Plus B has a larger surface area meaning that you cannot accelerate as quickly because your air resistance will have increased.

4.)  Is the force of air resistance larger in terminal velocity A or B? Why? Refer to Worksheet

It is the same because B and A have reached a constant velocity. Velocity is one of the things that affect the force of air resistance. Plus they are still both equal and opposite of the same f weight.

Practice Problems

1.)  Why does a steel ball hit the ground before a Ping-Pong ball?

Once they’ve both hit terminal velocity is when you will see the difference between the two balls. Until that point they are both traveling at the same speed. Once they’ve hit terminal velocity, the steel ball will continue to accelerate to a faster velocity to increase and equal the larger weight. While the Ping-Pong balls acceleration will start to decrease.

2.) What does a crumpled paper hit the ground before a flat sheet of paper?

The crumpled piece of paper has a smaller surface area than the flat sheet of paper. The flat sheet then has a greater f air and a lower net force, which means the acceleration, will be slower. If the acceleration is slower then it will take the flat sheet a longer time to fall after reaching terminal velocity. If acceleration is slower that means the velocity won’t increase in a great of a rate as the crumpled sheet of paper.

 Throwing Things Straight Up (Free Fall)

1.)  How do you find the height of a ball being thrown straight up?

First you find the total distance fallen. Then you calculate the distance fallen to the point of interest. Afterwards, you take first number and subtract the number you got in step two.

2.)  What formula do you use to find the distance?

d= ½(g)(t^2) 

3.)  If air resistance can be neglected, how does the acceleration of a ball that has been tossed upward compare with its acceleration if simply dropped?

The acceleration rate will decrease by 10 m/s^2 each second while the acceleration rate of a free falling object will continue to increase by 10 m/s^2 each second.

4.)  By how much does the speed of a ball decrease while going in the upward direction? When a ball is falling, how much does it increase?

The balls speed decreases by 10 m/s each second while ascending and increases by 10 m/s each second while descending. One more second is required for ascending than descending because it’s starting from zero.

5.) What is the velocity of the ball at the top of its path?

     The velocity is at 0 m/s at the top of its path. This is because it has reach equilibrium.

Examples and Practice Problems

1.)  You toss a ball straight up with an initial speed of 30m/s. How high does it go and how long is it in the air (neglecting air resistance) ?

To figure out the time in the air, just draw is out or use the formula d=1/2gt^2….

To figure out how high is goes you need to use the formula d=1/2 (g)(t^2).

Step one: d= ½ (g)(t^2)

d= ½ (10)(3^2)

d= ½ (10)(9)

d= ½(90)

d= 45 meters

2.)  A ball is tossed with enough speed straight up so that it is in the air several seconds….

a.)   What is the velocity of the ball when it reaches its highest point?

The velocity is 0 m/s

b.)  What is its velocity 1 second before it reaches its highest point.

        The velocity is 10 m/s

c.)   What is the change in its velocity during the 1-second interval?

The change is 10 m/s.

d.)  What is its velocity 1-second after it reaches its highest point?

                           The velocity is 10 m/s.

e.)   What is the change in its velocity during the 2-second interval? (Careful!)

The change is 20 m/s.

f.)    What is the acceleration of the ball during any of the timer intervals and at the moment the ball has zero velocity?

     The acceleration is 10 m/s^2.

Falling at an angle (Free Fall) (Projectile Motion)

1.) When an object has constant acceleration when falling (vertical), what do you use to find the velocity?

The formula you is v= 1/2gt

2.) What do you use to find the distance?

The formula you use is d= 1/2 gt^2

3.) When moving with a constant velocity (horizontal), what formula do you use to find the velocity?

           The formula used is v=d/t.

 4.) What formula do you use to find the distance?

 

            The formula you use is d=vt.

5.) What determines the time in the air?

The vertical velocity controls the time in the air.

 6.)  What are the special triangles you are likely to find?

You are likely to find 1-1-1 root 2 and 3-4-5 triangles. Now remember that the root of 2 is 1.41 in decimal form.

7.) What do you use to calculate how long the object will be in the air? Why?

To calculate how long an object will be in the air, use the formla d= 1/2gt^2. This is because we would already know the distance and the acceleration. We already know the acceleration because the acceleration of any free falling object Is 10m/s^2. We already know the distance because it will be stated already.

8.)   How do you calculate how far downfield an object will get after it is dropped (assuming it has some sort of an initial horizontal velocity)?

You will use the formula v=d/t. 

9.)  Why do you use 1/2gt^2 and v=gt for the vertical distances and velocities but rather v=d/t for the horizontal distances and velocities?

We use the formulas for the vertical distances and velocities because it has a constant acceleration of 10 m/s^2 while an object traveling horizontally may not have a constant acceleration, but it will have a constant velocity.

1    10.) Why does an object have a constant acceleration in the vertical direction?

This is because an object going downward in the vertical direction is considered a free falling object if we are neglecting air resistance. The acceleration of a free falling object will always be 10 m/s^2.

1    11.)  Why does an object have a constant velocity in the horizontal direction rather than a constant acceleration?

            

      This is because it is not a free falling object and there is no force acting on it that could increase it’s rate of acceleration.

1     12.) What kind of path does an object actually take?

         The object takes a diagonal path.

13.) Why do a bullet and its shell hit the ground at the exact same time even though the bullet travels farther down field? 

They hit the ground at the exact same time because they fall from the exact same height.

Examples and Practice Problems

You are on spring break with all of your friends and possible crushes. You are all about to jump off of a cliff, but before you do you dropped a shiny pebble to get the height. You find it is about 80 meters tall. After deciding that is a safe height, you run off of the cliff at a velocity of 20 m/s. How long were you in the air? How far from the cliff were you when you hit the water? 

'How long were you in the air? 

First use the formula d=1/2gt^2 

80= 1/2(10)(t^2) 

80= 5 (t^2) 

80/5= t^2

16= t^2

t= 4 seconds 

How far from the cliff were you when you hit the water?

To figure this out, use the formula v= d/t. 

20=d/4

20(4)=d

d= 80m 

Throwing Things Up at an Angle (Free Fall) 

1.) For objects thrown up at an angle, what controls the time in the air? 

    

     The velocity controls the time in the air. 

2.) What is one way in which objects being thrown up at an angle are different than objects being thrown straight up? 

    Objects at an angle have a constant velocity while object being thrown straight up have a velocity that decreases going up and increases going down.  

3.) The vertical velocity of an object being thrown straight up and at an angle is 0 m/s, however the object being thrown up at an angle is still moving. How is this possible? 

They have reached equilibrium. This means they can have a constant velocity of 0 m/s, but still be moving. 

4.) What formulas do you use to calculate the vertical velocities, distances, and times? 

    The formulas are v=gt and d=1/2gt^2. 

5.) what formulas do you use to calculate the horizontal velocities, distances, and times? Why is this is different from the ones you use to calculate the vertical velocities?

    The formula is v=d/t. You just have to rearrange it based on what you are trying to find. This is different because vertical objects are free falling objects, the acceleration will always be 10 m/s^2.  This is because the only force acting on it is the force of gravity with out the force of air resistance. While a horizontal object has forces acting on all sides with air resistance. 

6.) What are the two special right triangles we use? 

      If you do not remember this, return to the previous section and redo those problems. After you correct and check the questions, you may return and answer this again. 

Example and Practice Problem 

1.) You throw your dogs tennis ball up at a 45 degree angle. The ball has a velocity of 20 m/s in the horizontal direction, and 40m/s of speed in the vertical direction. How long will it be in the air? How fast will it be moving at the top of its path? How far downfield will it land? 

For this situation you can draw the picture instead of using a formula if you would like, but if you would like to use the formula you may.

Answer: The ball was in the air for 8 seconds! 

How fast will the ball be moving at the top of its path? 

The ball will be moving at 0 m/s at the top of it's path because it will have reached equilibrium. 

How far down field will it land? 

To figure this out, you need to use the formula v=d/t. 

Step one: 

20 = d/8 

d= 20(8)

d= 160m 

Answer: 160 meters 

Unit One Summary

In this unit I learned about 5 key concepts in Physics...

1.) Inertia/Newton's 1st Law

2 Net force and Equilibrium

3.) Velocity

4.)  Acceleration

3+4.) Constant Velocity vs. Constant Acceleration

5.) Using a graph (the equation of a straight line) to solve problems

In each of these concepts,  I learned a significant amount of info, formulas, and how they can be applied to everyday situations. In order to avoid confusion, I will break it all down into an easier format for myself and for whoever may read this post. Let's begin with Inertia/Newton's 1st Law!

Part one: Inertia/ Newton's 1st Law 

1.) What is Newton's 1st Law?

    Newton's 1st Law states (the Law of Inertia) ," an object at rest or an object in motion will remain   at rest or in motion at the same speed in the same direction, until acted upon by an outside force."

2.) What is mass?

      Mass is the measure of Inertia.

3.) What are the units for measuring mass?

     The units are Kg (Kilograms)

4.) How are Inertia and mass related?

    Mass is the measure of Inertia. Let's say there was a box. The mass would tell the student the    amount of stuff in the box, at rest or in motion.

5.) What is force?

      Force is how hard an object is pushed or pulled.

6. ) What are the units for measuring force?

       N (Newtons)

Examples & Practice Problems 

1.)  Go watch the video under the title," Newton's First Law of Motion:Inertia." Then read the explanation below the video or the explanation posted here. If one is unable to watch the video, I have summarized what occurs in the video and why, down below.

In that video, the playing card was resting on the cup with a penny placed in the center of the card.
The person then flicked the card and the penny fell straight down. The main question here is, why did the penny fall straight down, even though an external force moved the card off of the cup? To answer that one must understand a few things. In the video, the card and the penny were at rest.
 According to Newton's First law, " an object at rest or an object in motion will remain at rest or in motion unless acted upon by an external force."The objects were at rest because gravity was pushing down on the card/penny and the normal force counteracts the force of gravity. This means the forces were balanced. When the hand (the external force) acts upon the card, the card is then in motion and will remain in motion until acted upon by an outside force. The coin fell straight down because due to the absence of the card, there wasn't a large enough force to balance out the force of gravity. Therefore, the penny fell straight down because of an imbalance in forces.


2.)  You accidentally leave a Starbucks cup of coffee on the trunk of your car. When you take off it falls to the ground. Why do you find it on the ground below where you were parked?

The car and the coffee cup are both at rest. This means the forces are balanced. Then an outside force acts upon the car to set it in motion. However, there was no outside force acting on the coffee cup, so it stayed at rest. This is an example of Newton's First Law. The law states that " an object at rest or an object in motion will remain at rest or in motion unless acted on by an external force." So the coffee cup fell to the ground because below where you parked because the force of the car pushing up was no longer there to counteract the force of gravity. Therefore, it fell straight down where it was originally at rest.

3.)  A crate is sitting at rest. You push on the crate with 100N and the crate doesn't move. What is the force of friction on the crate that opposes your push? How do you know this?

The force of friction opposing the crate must be 100N. I know this because if forces are pushing in opposite directions and the object doesn't move then it is at equilibrium.

Part Two: Net force & Equilibrium

1.) What is Net force?

     Net force is the sum of all of the forces on an object.

2.) What is Equilibrium?

     Equilibrium occurs anytime the net force adds up to 0 Newtons.

3.) What is a force?

     A force is a push or a pull.

4.) What is the amount of force and the units of measurement?

      The amount of force is how hard something is being pulled or pushed and is measure in Newtons or (N). In addition, 1/4 lbs. = 1N.

5.) Are force and Kg related?

 No, they are not related because kg is, as stated in part one, the mass. The mass, again, tells us how much stuff is in the box. It doesn't not tell us the force being applied on the box. So remember that mass has nothing to do with force!

6.) What is difference between weight and mass?

     The weight of an object tell us the force the earth is pulling down will, while mass is the measure of inertia.

7.)  Can something be moving and not have any forces acting on it?

      Yes, a rock traveling through space. This is because in space, there is no gravity to act upon the rock nor any forces that could stop it.

8.) Can something be moving and have a net force of zero acting on it?

     Yes, Something in which either friction or an opposite force counteracts the force already acting on the object. 

Examples & Practice Problems 

1.)  Imagine there are two boxes!

- Box one: It has 5N of force pushing on the upper left side and 5N of force pushing on the lower left side of the box. When the force are going in the same direction, add them up. 5N+5N=10N. This means the goal net force on the box is 10N. Therefore, it is not at equilibrium and the force is causing it accelerate (speed up or slow down).


- Box two: This has 5N of force pushing on the left side of the box and 5N of for pushing in the opposite direction on the right side of the box. When forces are going in opposite directions, you must subtract one force from the other. 5N-5N= 0N. When the force is 0, the object is at equilibrium. This means the object could be at rest or at a constant velocity.

2.)  Imagine you board a hovercraft ride at the carnival. First, a large bulky football player gets on. The staff appointed to stop the rider seem to struggle to stop him. Then a little six year old girl gets on. The staff have no trouble stopping her. Why was she easier to stop than the large football player?

    The little girl likely weighs 60 lb. Therefore, gravity has to pull down with only 60 lb. in order to keep her on the ground. Now when she is sitting on the hovercraft, she is at rest. The external force acting upon her and the hovercraft, in order to put her in motion, has to be more than her weight to upset the balance in forces. Now to stop her, it'll take the same amount of force to stop her. If the football player weighs 300 lb. it would take a lot more force to stop him. Since 1/4 lb= 1N.


Part three: Velocity & Speed

1.) What is the formula to measure the speed of an object?

     The formula used is d/t=s or distance/time = speed.

3.) What is the formula used to find the velocity of an object?
   
       The formula used is the same, d/t=v or distance/time=velocity. Now using that formal we can also find the time and the distance of an object. To find distance, the formula is now d=(v)(t). To find the time, the formula is now d/v=t.

2.) How can speed be measured?

    The speed is measured using, mph (miles per hour), Km/h (kilometers per hour), m/h (meters per hour), m/s (meters per second), cm/s (centimeters per second).

3.) In physics, what is the common measurement of speed?

     The common measurement is m/s.

4.) Compare and contrast speed and velocity

    They both measure m/s and talk about the distance covered in a given time. Now velocity requires a specific direction while speed does not.

5.) What are the arrows often seen in physics diagrams?

    The arrows are called vectors. They are used to show how much of something or the magnitude (how great the velocity is). In addition, they show direction.

6.) What is a major difference between constant acceleration and constant velocity?

     An object at constant velocity requires a specific direction, while constant acceleration does not.

7.) Does changing velocity require a force?

    Yes, because an external force was required to set it in motion.

8.) How does an object change velocity?

    There are three ways to change velocity. The object must change direction, speed up, or slow down.

Examples & Practice Problems 

1.)  A race car is going around and around the track at 100 mph. Does it have a constant speed or a constant velocity?

     When the car turns the corner it is changing direction. Therefore, the car is constantly changing direction. When an object is changing direction it can no longer be at a constant velocity, since velocity requires a specific direction. That is why it is at a constant speed instead.


2.) A bicycle rides for 1 hour at 5 mph. Then for 3 hours at 4 mph and finally for 2 hours at 7 mph.

       - How many miles did you ride?

 In order to find the distance use the formula, (t)(v)= (d) or (time)(velocity)= (distance).
So (5)(1)= 5, (3)(4)= 12, (2)(7)= 14. Then add 14+13+5= 32!

3.)  A car maintained a constant velocity of 100 m/s!

      How fast was the car going after 10 seconds?

 4.) If a car is maintaining a constant velocity, then it will still be going 100 m/s no matter what time it is.

 5.)  How far did the car go after 10 seconds?

 Using the formula (v)(t)= d, we can then use substitution to get  (10)(100)= 1,000 meters.


Part four: Acceleration 

1.) What is acceleration and how do I find it?

      The change in velocity (speeding up, slowing down, or changing direction) over a certain time interval.

2.) What are the units for acceleration?

     The units are meters per second squared or m/s^2.

3.) What is the formula used to find out how fast an object is going? (used only when the the acceleration is constant)

The formula used is v=(a)(t) meaning velocity= (acceleration)(time).

4.) What is the formula used to find out how far (the distance) of an object? (used only when the acceleration is constant)

     The formula used is d=1/2(a)(t^2) meaning distance= 1/2 (acceleration)(time squared).

5.) What are the three ways someone can identify acceleration?

      The three ways are if an object is slowing down, speeding up, or changing direction.

6.) What is the acceleration of an object falling straight down?

     The acceleration is 10 m/s^2 for all free falling objects!

Examples & Practice problems 

1.)  A ball is just rolling down the highway, and there isn't any friction  to take into account, what is the acceleration of the ball. How do you know?

     The acceleration of the ball is zero because if a ball is accelerating it must be speeding up, slowing down or changing directions. The ball is not speeding up, slowing down, nor is it changing directions. If the velocity is constant then their can be no change in acceleration.

2.) You are watching a soccer game and you see a player kick the ball. You notice the following...

at 0s it is moving at 0m/s

at 1s it is moving at 4 m/s 

at 2s it is moving at 8 m/s 

  at 3s it is moving at 12 m/s 

-Question: what is the acceleration and how do you know?

Tip: To figure out the acceleration, divide the change in velocity by a certain interval of time. To find the   change in velocity, we subtract the velocity of the first observation from the velocity of the second observation. Using that strategy we can also find the interval of time!

Step one: 8 m/s- 4 m/s = 4 m/s (the change in velocity)

Step two: 2s-1s= 1s (the interval of time)

Step three: 4 m/s (the change in velocity)/ 1s (the interval of time) = 4 m/s^2

Answer: 4m/s^2

3.) If a ball was rolling at the end of the ramp with an acceleration of 4 m/s^2 and rolled for 5s.
   
- How fast was it rolling at the end of the ramp?

Tip: To figure this out, we need to use the formula (v)= (a)(t), and then substitute what we already know.

  Step one: v= (4m/s^2)(5s)

  Answer: v= 20 m/s

- How far did it roll during this time?

Tip: To figure this out, we need to use the formula d=1/2(a)(t^2), and then substitute what we already know.

Step one: d= 1/2 (4m/s^2)(5s^2)

Step two: d= 1/2 (4m/s^2)(25s)

Step three: d=1/2 (100m)

Answer: d= 50m

Part 3+4: Constant Velocity vs. Constant Acceleration 

1.) What are the formulas used when an object is maintaining constant velocity?
   
     How far: d=(v)(t)    

    How fast: v=d/t

2.) What are the formulas used when an object is maintaining a constant acceleration?

     How far: d=1/2(a)(t^2)

     How fast: v= (a)(t)

3.) If something has constant velocity, can it have constant acceleration? Why or why not?

      It cannot because an object maintaining a constant velocity is covering the same distance at the same rate in the same amount of time. While an object maintaining constant acceleration, would be increasing or decreasing its speed by the same rate. Therefore, it would be covering a greater distance each time, but within the same amount of time.

4.) If something has constant acceleration, can it have constant velocity.

    The answer is the same as number three.

5.) If something has increasing acceleration, is its velocity increasing, decreasing, or constant?

    The velocity would be increasing.

6.) If something has decreasing acceleration, its velocity increasing, decreasing, or constant?

     The velocity is increasing because the object is still accelerating. The object is just not accelerating as quickly as it was.


Example & Practice Problem 

1.) After analyzing the two situations below, decide which one is an example of constant acceleration and which one is an example of constant velocity. Explain your answer!

Situation one:

A glass sphere is just rolling on a crystal floor in the white house.


Situation two:

- You are enjoying a nice sunny day, on top of one of our many luscious hills, with your pet hamster. He is sleeping in his little plastic ball, but after a while you forget he is there! You get ready to leave and sling your backpack on, but it hits his ball. The ball begins to roll down the steep hill.

You observe the following....

at 0s it is moving at 0 m/s 

at 1s he is moving at 6 m/s 

at 2s it is moving at 12 m/s 

at 3s it is moving at 18 m/s 

Answer Situation one: This is an example of constant velocity because the surface is flat and there is no friction.

 Newton's first law best supports why know the object is maintaining a constant velocity! According to Newton's first law states, " an object at rest or in motion will remain at reset or in motion at the same speed in the same direction until acted upon by an outside force." As we know from the "Speed and Velocity" section, if an object is going in the same direction at thee same speed then it is maintaining a constant velocity because for an object to maintain a constant velocity, the object must remain maintain speed in one direction. If the objects changes direction it is now maintaining a constant speed. Think of it like a race car going around a track. The car maintains the same speed, but changes direction every time he goes around a turn on the race track.

Answer Situation two: This is an example of constant acceleration because the ball is increasing in speed, but by the same amount and it may change direction. To prove this, we can use the formula
v=(a)(t).

6m/s=(?)(1s)
(6m/s)/(1s)= 6m/s^2

12m/s^2=(?)(2s)
(12m/s)/ (2s)= 6m/s^2

18m/s=(?)(3s)
(18m/s)/ (3s)= 6m/s^2

Answer: We can see here that the ball is increasing in speed each time, but it is also increasing by 6m/s^2 within each interval of time.


Part 5: Using a graph (the equation of a straight line) to solve problems

1.) What is the equation for a straight line?

      y=mx+b

2.) How does velocity equal slope?

    Velocity equals (distance)/(time).  The slope is rise/run or in other words
(the change in y)/ (the change in x).  In this equation.....

- y= distance

- m= the slope

- x= the time

-b= the y-intercept.

3.) In the equation, d=1/2(a)(t^2) what part  of this equation represents slope?

The acceleration represents the slope. In other words, 1/2 of the acceleration equals the slope.

Example 

Example one: Compare the two graphs below and label each one either constant acceleration or constant velocity.


Graph one

Graph two 

Comparison: Graph number one is constant velocity, while graph number two is constant acceleration. Graph number one has a straight line because the object maintained the same speed in the same direction constantly. Therefore, it covered the same distance in the same amount of time. While in graph number two, the object covered a greater distance in the same amount of time, increasing in speed with each interval of time. That is why the line is gradually getting higher, while the line in constant velocity remains straight.