Laboratory: MOTION in ONE DIMENSION

LAB: MOTION IN ONE DIMENSION (2014)

1. On a sheet of graph paper make a graph of position vs. time.

Draw predictions for each of the following motions on the same graph.

a) Start at the 0.5 meter mark and walk in the + direction slowly and steadily. b) Start at the 0.5 meter mark and walk in the + direction quickly and steadily. c) Start at the 3 meter mark and walk in the - direction slowly and steadily. d) Start at the 3 meter mark and walk in the - direction quickly and steadily.

2. Now, make a different graph showing velocity vs. time.

Draw predictions for the same motions on this new graph

e) Start at the 0.5 meter mark and walk in the + direction slowly and steadily. f) Start at the 0.5 meter mark and walk in the + direction quickly and steadily. g) Start at the 3 meter mark and walk in the - direction slowly and steadily. h) Start at the 3 meter mark and walk in the - direction quickly and steadily.

3. You have just made your predictions for the motions described.

Now, we‘ll verify our predictions using the Sonic Range Finder (motion detector). To do so, set up the equipment, then open the Logger Pro software. The appropriate graphs should appear on screen. (x vs t and v vs t)

Use the motion detectors to check and see if each of the 8 predictions you made in parts 1 and 2 above were correct.

Explain your interpretations of the graphs as compared to your predictions. Remember to elaborate.

In the lab report, you will need to include your predictions, the actual graphs made on screen, and your explanation of the results. 4. The next thing we’re going to do is try to physically reproduce a motion to match a position vs. time graph given to us by the computer! Open the file “01b” to do some graph matching.

Predict how you will specifically have to move to match the data shown on the screen. Your predictions need to be specific, and written down.

For example: “stand at the 0.5 meter mark for 2 seconds, then move steadily to a point 3 m away from the detector over a 1 second period. Remain at the 3m position for another second, then move slowly toward the detector for …”

When you’ve finished writing your prediction, test your prediction using the motion detector. Match it closely!

Repeat with “01c”.

5. After we’ve mastered position time graphs, we’ll try to physically reproduce a motion based on a velocity vs. time graph

Open the file “01d”. As a group, predict how you would have to move (be specific!) to match the data shown on the screen.

Test your prediction, using the motion detector set up.

Repeat through “01g”.

For graphs b-e, calculate the average velocity for the entire motion shown on the graph. This may be tricky for some of the graphs, stick with it! Exit Questions

1. James Bond is being chased by the KGB. He has a head start and runs as fast as he possibly can but the KGB agent runs faster and eventually catches the aging Bond. Represent the story graphically on another sheet of paper. Then, with words, explain what your graph depicts.

2. The story of three bicyclists is represented by these 3 motion diagrams. The numbers represent time in seconds. The dot placement shows where the bike is at that time.

0 1 2 3 4 5

5 4 3 2 1 0

Represent the story in words, and also graphically on position vs. time axes. Did bicycle 1 meet bicycle 3? At what time did this happen?

3. a) Describe the difference between the graphs (position and velocity) you made by walking away slowly and the ones made by walking away more quickly.

b) Describe the difference between the graphs (position and velocity) made by walking toward and the one made walking away from the motion detector.

c) Does your initial position affect your data in the position match? Does your initial position affect your data in the velocity match? Explain.

4. A person walks 5 km to the west, then 1 km south, 3km east and the last km is north. This entire walk takes 4 hours. What was the person’s average velocity? What was their average speed?

5. An object moves from Point A to Point B with an average velocity of vavg. Is it possible at any point during the trip that the object had a velocity greater than vavg? Explain… Exit Questions - Part II + V e 0 Time l - 1. How do you move to create a horizontal line in the positive part of a velocity-time graph, as shown above?

+ V e 0 T i m e l - 2. How do you move to create a straight-line velocity-time graph that slopes up from zero, as shown above?

+ V e 0 T i m e l - 3. How do you move to create a straight-line velocity-time graph that slopes down, as shown above?

+ V e 0 T i m e l -

4. How do you move to make a horizontal line in the negative part of a velocity-time graph, as shown above? Sketch the velocity vs. time graphs corresponding to each of the following descriptions of the motion of an object. No numbers needed, just a general sketch.

+ 5. The object is moving away from y t i the origin at a steady (constant) c

o l velocity. e 0V Time

+ 6. The object is standing still. y t i c o l 0e V Time

+y t 7. The object moves toward the i c o origin at a steady (constant) l e

V velocity for 10 seconds, and then 0 10 20 Time stands still for 10 seconds. (sec) -

8. The object moves away from the t i c

origin at a steady (constant) o l e

velocity for 10 seconds, reverses 0V Time direction and moves back toward 10 20 (sec) the origin at the same speed for - 10 seconds. 9. Draw the velocity graphs for an object whose motion produced the position-time graphs shown below on the left. Position is in meters and velocity in meters per second. Note: Unlike most real objects, you can assume these objects can change velocity so quickly that it looks instantaneous with this time scale.

* The graphs you draw for v vs. t should match the exact velocities shown in the x vs. t *

4 +2 )

3 ) s m

/ +1 (

m n ( o i

2 y t t i i s

c 0 o o 1 2 3 4 5 l P 1 e Time(sec) V -1 0 0 1 2 3 4 5 -2 Time (sec)

4 +2 )

( s +1 / n m o ( i

t 2 i y t s i

o 0 c 4 P o 1 2 3 5 l 1 e Time(sec) V -1 0 2 0 1 3 4 5 -2 Time (sec)

4 +2 ) m

3 ) ( s

/ +1 n o m i ( t

i 2 y s t i o

c 0 P o 1 2 3 4 5 l 1 e Time(sec) V -1 0 0 1 2 3 4 5 -2 Time (sec) 10. The object moves with a steady (constant) n o

velocity away from the origin. i t i s o P

0 T i m e

11. The object is standing still. n o i t i s o P

0 T i m e

12. The object moves with a steady (constant) n o i t velocity toward the origin for 5 seconds and i s o

then stands still for 5 seconds. P

0 T i m e

13. The object moves with a steady velocity

away from the origin for 5 seconds, then n o i t

reverses direction and moves at the same speed i s

toward the origin for 5 seconds. o P

0 T i m e

14. The object moves away from the n o

origin, starting slowly and speeding i t i

up. s o P

0 T i m e 15. What do you do to create a horizontal

line on a position-time graph? n o i t i s

T i m e

16. How do you walk to create a straight line

that slopes up? n o

o P T i m e

n o i t i s

o 17. How do you walk to create a straight line P

that slopes down? T i m e

n o i t i s

o P 18. How do you move so the graph goes up steeply at T i m e first, and then continues up gradually?

19. Explain in detail why acceleration is measured in m / s2 and not m / s .

For the velocity vs. time graph above, circle (or otherwise identify) the speeding up parts. 21. a) The area ‘under’ the v vs. t graph gives information about what?

b) Use your answer from a) above to explain where x = ½ (vi + vf) t comes from.

c) Show using algebra that x = ½ (vi + vf) t is the same as vavg = x / t