Constructing/Analyzing Motion Graphs
1. Consider the position-time graph below for two cyclists, Alice and Ben.
/ a. Do the cyclists start at the same point? ___ If not, which one is ahead at the beginning?b. At t= 7s, which cyclist is ahead? ______
c. Which cyclist is traveling fastest at 3 s? ______How do you know?
d. Are the velocities of the two cyclists equal at any time? __
e. Describe the situation at the intersection of lines A and B.
2. Consider the position-time graph below for a different trip made by Alice and Ben.
/ a. How does the motion of Alice in this graph compare to her motion in the previous graph?b. How does Ben’s motion compare to the previous graph?
c. Which cyclist is traveling the fastest? How do you know?
d. Describe what is happening at the intersection of lines A and B.
e. Which cyclist has traveled further during the 5 five seconds? ___
3. Robin, roller skating down a marked sidewalk, was observed to be at the following positions at the times listed in the data table below. Graph the data (don’t forget labels) and answer the related questions. (See Instructor for Solutions)
Time(s) / Position (m) / / a) How far from the origin was he at t = 6.0 s? ______
0.0 / 10.0
1.0 / 12.0
2.0 / 14.0
5.0 / 20.0 / b) Was his speed constant over the entire interval? How do you know?
8.0 / 26.0
10.0 / 30.0
c) How fast was he traveling from t = 2.0 s to t = 8.0 s?
Consider the motion given by the position-time graph shown below to answer questions 4-12.
- (I) Is the object ever at rest? ______If so, when? ______
5. (I) Where is the object at the end of this trip? ______
6. (I) When is the object going the fastest? ______
7. (II) Are there any times during which the object is moving at the same speed? ______
If so, when? ______
8. (II) Are there any times during which the object is moving with the same, (nonzero) velocity? ______
If so, when? ______
9. (II) What is the average speed of the object for the entire trip? ______
10. (II) What is the average velocity for the object for the first 10 seconds? ______
11. (II) What is the instantaneous velocity at t = 15 s? ______
12. (II) Draw the velocity-time graph for the same motion illustrated in the position-time graph above.
4) yes t = 5s – 10s and t = 20s – 25s / 5) position +20 m / 6) t = 0s – 5s7) yes t = 10s – 20s and t = 25s – 30s / 8) no / 9) 2.00 m/s
10) +3.00 m/s / 11) – 2.00 m/s / 12) See Instructor
Consider a new motion … given by the velocity-time graph shown below … to answer questions 13 - 20.
13. (I) When was the object moving with constant speed? ______
14. (I) When was the object at rest? ______
15. (I) Was the object ever moving left? ______If so, when? ______
16. (I) What was the velocity of the object at t = 1 s? ______at t = 5 s? ______
17. (II) What was the acceleration of the object during the first 2 s? ______
18. (II) What was the displacement for the first 8 s? ______
19. (II) What was the displacement for the entire trip? ______
20. (II) Draw the acceleration-time graph for the same motion represented by the velocity-time graph above.
0 4 8 12 16 20
Time (s)
15) t = 2s – 8s t = 16s – 18s / 16) t = 10s – 14s / 17) t = 14s – 20s18) 1m/s; 2m/s / 19) 1m/s2 / 20) 14m
21) 8m / 22) See Instructor
21. Consider the position-time data in the table below. Prepare a position-time graph and a velocity-time graph on the axes given.
Time (s) / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9Position (m) / 0 / 2 / 4 / 4 / 7 / 10 / 10 / 10 / 5 / 0
/ / a) Use the x-t graph to determine the displacement from
t = 0 s to t = 3.0 s.
b) Determine the area under the v-t graph from t = 0 s to
t = 3.0 s.
c) Use the v-t graph to determine the displacement from
t = 3.0 s to t = 5.0 s
d) What is the average speed for the first 5 s?
e) What is the average velocity for the entire 9 s?
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