motion graph assignment answer key

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The moving man - answer key

Physics 15a (phys 15a), harvard university.

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Name Answer Key Period Date Motion Simulation: The Moving Man Through a web browser, navigate to Click with then then then choose the 2 seconds simulation. Click to start the simulation. Object of the simulation 0 meters 2 To explore position and velocity graphs of an object moving in different Position 2 m I ways. Velocity 234 Acceleration 0 Familiarization There are two tabs for this simulation, called and For activity, you will need only the tab. Play with the controls of the simulation to get used to the controls. Can you find two ways to move the man around? how to make the man move automatically? how to record and playback the motion? how to playback the motion in slow motion? how to quickly reset the man to starting conditions? Constant Velocity 1. Reset all of the values to zero. 2. Using the position slider, set the man to stand near the tree. Give him a velocity of 1 (and an acceleration of 0). 3. Click to start the man in motion until he hits the wall, then hit II to stop recording. 4. Use the playback feature to answer these questions. a. What happened to the blue position slider as the man moved across the screen? Increases slowly. (moves to the right) b. What happened to the red velocity slider as the man moved across the screen? Stays at zero. Name Answer Key Period Date Motion Simulation: The Moving Man Through a web browser, navigate to Click with then then then choose the 2 seconds simulation. Click to start the simulation. Object of the simulation 0 meters 2 To explore position and velocity graphs of an object moving in different Position 2 m I ways. Velocity 234 Acceleration 0 Familiarization There are two tabs for this simulation, called and For activity, you will need only the tab. Play with the controls of the simulation to get used to the controls. Can you find two ways to move the man around? how to make the man move automatically? how to record and playback the motion? how to playback the motion in slow motion? how to quickly reset the man to starting conditions? Constant Velocity 1. Reset all of the values to zero. 2. Using the position slider, set the man to stand near the tree. Give him a velocity of 1 (and an acceleration of 0). 3. Click to start the man in motion until he hits the wall, then hit II to stop recording. 4. Use the playback feature to answer these questions. a. What happened to the blue position slider as the man moved across the screen? Increases slowly. (moves to the right) b. What happened to the red velocity slider as the man moved across the screen? Stays at zero. Name Period Date 5. Use the playback feature to record the position and velocity data. Time (s) Position (m) Velocity 0 1 1 1 2 7 1 3 1 4 1 5 1 6 1 7 1 8 1 9 0 1 10 200 1 6. Plot your data in the graphs below: 8 4 0 0 2 4 6 8 10 Time (s) : 2 Straight horizontal 1 line at 0 1 7. According to your graphs a. What shape is your position graph? A straight line. b. What is the slope of your position graph? Slope 1 C. Why does or answer to b: make sense? set at 1 That means for every record, the This makes your sense because the velocity was d. What shape is your velocity graph? Is it horizontal, vertical, or diagonal? man moved Ahorizontal line. 1 meters. e. Why does or your answer to d. make sense? It makes sense because the velocity stayed the same for the entire time interval. Name Period Date 5. Use the playback feature to record the position and velocity data. Time (s) Position (m) Velocity 0 1 1 1 2 7 1 3 1 4 1 5 1 6 1 7 1 8 1 9 0 1 10 200 1 6. Plot your data in the graphs below: 8 4 0 0 2 4 6 8 10 Time (s) : 2 Straight horizontal 1 line at 0 1 7. According to your graphs a. What shape is your position graph? A straight line. b. What is the slope of your position graph? Slope 1 C. Why does or answer to b: make sense? set at 1 That means for every record, the This makes your sense because the velocity was d. What shape is your velocity graph? Is it horizontal, vertical, or diagonal? man moved Ahorizontal line. 1 meters. e. Why does or your answer to d. make sense? It makes sense because the velocity stayed the same for the entire time interval. Name Period Date 7. According to your graphs a. What shape is your position graph? A curved line. (This is actually part of a parabola.) b. Why does or your answer to a. make sense? This makes sense because every second, the speed is increasing. That means that the distance C. What shape is your velocity graph? he covers in each time interval A straight line. gets bigger and bigger. d. Why does or your answer to C. make sense? This makes sense because the acceleration is set to 0 This means every second, the speed e. What is the slope of your velocity graph? increases f. What does the slope of the velocity graph represent? The slope of a graph is acceleration. Making Connections 1. What happens to the man when he is accelerating? He moves faster and faster every second. 2. What is the difference between an object with constant acceleration and an object with constant speed? An object that is accelerating has a different speed for each time interval (faster faster). An object with constant speed always has the same speed. 3. Complete the following sentences: a. slope of a linear position graph tells us the SPEED of the (or velocity!) b. slope of a linear velocity graph tells us the ACCELERATION of the post vell. C. an object moving at a constant speed, we would expect to see a position graph with a time time straight line shape and a velocity graph with a horizontal d. an object moving at a constant acceleration, we would expect to see a position graph I vell. with a curved line shape and a velocity graph with a straight line. shape. time time Name Period Date 7. According to your graphs a. What shape is your position graph? A curved line. (This is actually part of a parabola.) b. Why does or your answer to a. make sense? This makes sense because every second, the speed is increasing. That means that the distance C. What shape is your velocity graph? he covers in each time interval A straight line. gets bigger and bigger. d. Why does or your answer to C. make sense? This makes sense because the acceleration is set to 0 This means every second, the speed e. What is the slope of your velocity graph? increases f. What does the slope of the velocity graph represent? The slope of a graph is acceleration. Making Connections 1. What happens to the man when he is accelerating? He moves faster and faster every second. 2. What is the difference between an object with constant acceleration and an object with constant speed? An object that is accelerating has a different speed for each time interval (faster faster). An object with constant speed always has the same speed. 3. Complete the following sentences: a. slope of a linear position graph tells us the SPEED of the (or velocity!) b. slope of a linear velocity graph tells us the ACCELERATION of the post vell. C. an object moving at a constant speed, we would expect to see a position graph with a time time straight line shape and a velocity graph with a horizontal d. an object moving at a constant acceleration, we would expect to see a position graph I vell. with a curved line shape and a velocity graph with a straight line. shape. time time

• Multiple Choice

Course : Physics 15a (PHYS 15A)

University : harvard university.

• More from: Physics 15a PHYS 15A Harvard University 405   Documents Go to course

Graphs of Motion

Practice problem 1.

Sample responses can be found on the second page of worksheet-compare.pdf , or by clicking on the image on the right.

practice problem 2

• What can we say about the motion of this object?
• Plot the corresponding graph of acceleration as a function of time.
• Plot the corresponding graph of displacement as a function of time.

The problem presents us with a velocity-time graph. Do not read it as if it was showing you position. You can't immediately determine where the object is from this graph. You can say what direction it's moving, how fast it's going, and whether or not it's accelerating, however. The motion of this object is described for several segments in the graph below.

Acceleration is the rate of change of displacement with time. To find acceleration, calculate the slope in each interval.

Displacement is the product of velocity and time. To find displacement, calculate the area under each interval.

Find the cumulative areas starting from the origin (given an initial displacement of zero)

Plot these values as a function of time. Pay attention to the shape of each segment. When the object is accelerating, the line should be curved.

practice problem 3

• an object moving with constant velocity . (Let the initial displacement be zero.)
• an object moving with constant acceleration . (Let the initial displacement and velocity be zero.)

Since the velocity is constant , the displacement-time graph will always be straight, the velocity-time graph will always be horizontal, and the acceleration-time graph will always lie on the horizontal axis. When velocity is positive, the displacement-time graph should have a positive slope. When velocity is negative, the displacement-time graph should have a negative slope. When velocity is zero, the displacement-time graph should be horizontal.

Since the acceleration is constant , the displacement-time graph will always be a parabola, the velocity-time graph will always be straight, and the acceleration-time graph will always be horizontal. When acceleration is positive, the velocity-time graph should have a positive slope and the displacement-time graph should bend upward. When acceleration is negative, the velocity-time graph should have a negative slope and the displacement-time graph should bend downward. When acceleration is zero, all three graphs should lie on the horizontal axis.

practice problem 4

• just before the parachute opened
• just after the parachute opened
• from the beginning of the jump to the time just before the parachute opened?
• from the time just after the parachute opened to the time when the skydiver landed?
• velocity-time
• acceleration-time

Questions about velocity.

There are at least two ways to determine the velocity just before the parachute opened. One would be to use the fact stated in the stem of the problem — that the skydiver was in free fall. We could use the first equation of motion for an object with a constant acceleration. Up is positive on this graph, so gravity will have to be negative.

We could also use the graph itself (instead of the description of the graph) to solve this part of the problem. In the last half second, from 6.5 to 7.0 seconds, the graph looks very nearly straight and the skydiver appears to drop from 90 to 60 meters. Slope is velocity on a displacement-time graph. Compute it.

So which answer is correct? Well neither. Free fall in an atmosphere is technically impossible, which means the first answer is only true in an idealized world. The second answer is definitely a mathematical approximation. We don't really know the slope of the tangent to the left side of 7 seconds. I said it sort of looks straight in the last half second, but sort of doesn't cut it. I think it's more likely that the skydiver was almost in free fall than the curve was almost straight in the last half second before the chute opened. If I were to ask this question of my students, however, I would accept both answers as reasonable and award full credit — as long as there were no other errors like missing units.

From 7 to 17 seconds, the graph is straight. Straight lines on a displacement-time graph indicate constant velocity. Velocity is slope on this kind of graph. Compute it.

This is the answer to this part of the problem. On this there can be no debate.

Questions about acceleration.

There appear to be 4 valid ways to determine the acceleration in the first 7 seconds. The first is to just agree with what the text description says. The skydiver is in free fall. Free fall acceleration on Earth is just a number — a number that you should memorize if you have a professional reason for learning physics.

a  =  −9.8 m/s 2

The second method uses the graph and an equation of motion. Since we're given a displacement-time graph, use the displacement-time relationship, a.k.a. the second equation of motion. After 7 seconds, the skydiver has fallen from rest a distance of 240 meters.

The third and fourth methods use the other two equations of motion. Since these rely on our choices for the final velocity, multiple valid answers are possible. Let's say we use the velocity calculated from the slope of a "tangent" with a value of −60 m/s and and the velocity-time relationship, a.k.a. the first equation of motion. Then…

We could also use the velocity-displacement relationship, a.k.a. the third equation of motion, with a final velocity of −60 m/s and a displacement of −240 m. That gives us…

I don't like these last two answers, but I'd have to accept them if a student gave them to me. They are valid answers given what the graph shows. Given how much they disagree with the other answers means they're probably "wrong", but so what? They aren't wrong because of faulty reasoning. They're wrong because of the limitations of the graph. Welcome to the real world.

After 7 seconds, life is easy. Look at the graph near the end. It's a straight line. Look at it again. Isn't it lovely? So straight. A straight line on a displacement time graph indicates constant velocity or zero acceleration. Let me compute it for you. Oh wait, there's nothing to compute. Draw a hole and add a unit to it.

a  =  0 m/s 2

Questions about the graphs.

Here's the original altitude-time, or displacement-time, or position-time or whatever-you-want-to-call-it graph. It's what I gave you to work with.

Here's the velocity-time graph. All the signs are negative. The velocity became more and more negative until the chute opened, then it was a smaller (but constant) negative number afterwards.

Here's the acceleration-time graph. The skydiver falls with a constant negative acceleration of −9.8 m/s 2 for 7 seconds, then she has no acceleration. No means zero meters per second squared. Constant values are horizontal lines on this graph.

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PhET The Moving Man KEY

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