Motion and Graphing
An activity from the Burroughs Wellcome Student Research Program The Science of Sports

Problem:

Motion is a major component of all sports. In fact the purpose of many sports is to move a ball or players to a specified position in order to score points. Often we describe motion using words: fast, slow, forward, backward, but as scientists we need a more quantitative method of describing motion. How can graphs be used to describe the motion of an object?

Introduction:

In general there are 3 different quantities that can be used to describe the motion of any object. These are displacement, velocity and acceleration. Each of these is a vector. That is they describe magnitude and direction. Magnitude is the amount or the number and direction is usually specified by + and - or, in 2 dimensions, degrees and radians.

Displacement is defined as the distance from a starting point. The magnitude is how far and the direction tells what 'side' of the starting point the object is on. For example 6 meters North.

Velocity is the rate of change of displacement or how much the displacement changes over time and depends on direction. Speed is similar to velocity except it does not depend on direction. 60 miles per hour is speed, however 60 miles per hour East is velocity. Velocity can be expressed by the formula:

v =	(D s)
	(D t)

where v = velocity in meters/second, D s = change in displacement in meters, and D t = change in time in seconds.

Materials
Computer ULI and MacMotion software OR LabPro and LoggerPro software Motion Detector meterstick wooden plank assorted masses books to support ramp toy car or cart masking tape basketball

Procedure:

ULI: Turn on the computer and the ULI. Insure that the Motion Detector is connected to Port 2 of the ULI. Once the computer is on, open the MacMotion program. Under Display, choose 2 Graphs and change the x-axis to 30 seconds (or longer if needed).

LabPro: Connect the LabPro and turn on the computer. Plug the motion detector into DigSonic1 of the LabPro. Once the computer is on, open the LoggerPro program. Under the Experiment menu select Show Sensors and choose the motion detector in the appropriate port. Change the x-axis to 30 seconds (or longer if needed).

Place the Motion Detector on the edge of the table facing into the room. To generate graphs start the computer by clicking the start button in the lower left hand corner of the screen. Stand about 0.5 m from the detector to begin. Once the detector begins clicking, one student begins walking in front of the detector and the computer plots the motion on the screen.

Exploring I: Constant Velocity

Use the computer to generate the velocity-time graphs and displacement-time graphs for the following situations. Sketch your results neatly on a piece of graph paper or print out the graphs.

Graph A: Walking slowly and steadily away
Graph B: Walking quickly and steadily away
Graph C: Walking slowly and steadily towards
GraphD: Walking quickly and steadily towards

Discussion I:

What is the major difference in the slopes of the displacement and velocity graphs when you are moving slowly and when your are moving quickly?

What is the major difference in the slopes of the displacement and velocity graphs when you are moving towards and when you are moving away from the detector?

Sketch the velocity and displacment graphs that would be produced for the following situation: A person starts 1 meter away from the detector and walks slowly away for 4 seconds. The person then stops for 4 seconds and walks towards the detector quickly. (Be sure to label and number the axes)

Now use the detector to record the motion described above and sketch the results.

How does predicted graph compare to the graph you just produced? Explain your answer.

Conclusions I:

How is velocity represented on Displacement graphs?

How is direction represented on Displacement graphs?

How is direction represented on Velocity graphs

Why are the graphs sometimes wavy instead of straight?

Exploring II: Accelerated Motion

Set up a ramp using the books and the plank. The high end of the ramp should be about 60 cm from the floor. Set the motion detector at the bottom of the ramp.

Record the velocity and displacement graphs of the basketball pushed up the ramp and allowed to roll back down. Catch the ball before it hits the motion detector. Sketch the graphs.

Describe the motion of the basketball.

Now place the detector at the top of the ramp. Predict what the graphs will look like for the same motion but viewed from the top of the ramp. For example instead of the ball moving away first, it is now moving towards.

Now test your prediction with the basketball and sketch the actual graphs.

Discussion II:

What is the major difference in the slopes of the displacement and velocity graphs when the ball is slowing down and when it is speeding up?

What is the major difference in the slopes of the displacement and velocity graphs when the ball is moving towards and when the ball is moving away from the detector?

Sketch the velocity and displacment graphs that would be produced for the following situation: A person starts 1 meter away from the detector and walks speeding up away for 4 seconds. The person then stops for 2 seconds and walks towards the detector Speeding up for 2 seconds and slowing down for 2 seconds. (Be sure to label and number the axes)

Now use the detector to record the motion described above and sketch the results in the graphs.

How does predicted graph compare to the graph you just produced? Explain your answer.

Conclusions II:

How is acceleration represented on Displacement graphs?

How is acceleration represented on Velocity graphs?

When is acceleration positive? When is it negative?