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Accelerated Motion Worksheet Answers
General Physics (PHYS 1120)
University of Nebraska at Omaha
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Uniformly Accelerated Particle Model Worksheet 4:
Interpreting Graphs of Accelerated Motion
Object A:
a. Where on the graph above is the object moving most slowly? How do you know?
The object is not moving at locations B and F. We know this because the slope of the tangent is zero (in other words the curve is horizontal at those points). If the student interprets the question to mean where is it actually moving but at the slowest rate, the locations would be just before and after B and F. Reasoning is that the slope is very small.
b. Between which points is the object speeding up? How do you know?
The object is speeding up between B and C and also between F and G. We know this because between those points the slope is continually increasing in steepness.
c. Between which points is the object slowing down? How do you know?
The object is slowing down between A and B and also between E and F. (and also after G) We know this because between those points the slope is continually decreasing in steepness.
d. Where on the graph above is the object changing direction? How do you know?
The object is changing direction at B and F. We know this because the slope is going from negative to positive or positive to negative at these points.
A
B C
D
E F
G
position
time
a. Give a written description of the motion.
Object B is starting from rest at the 25m position and speeding up in the negative direction.
b. Represent object B’s motion with a motion map. Include both velocity and acceleration vectors.
c. Find the displacement from t = 2 s to t = 8.
At 8s the position is 9m and at 2s it is 24m. x x x m mf i9 24 15 m
d. Find the average velocity from t = 2 s to t = 8.
- 8 2.
m s
x m v t s s
e. Find the instantaneous velocity at t = 2 s and t = 8 by finding slopes of tangents. To find the slope of the tangent I will find the slope of the secant where the midtimes are 2 and 8s.
2
21 25.
1.
4 0.
m s s
x m m v t s s
8
0 16. 4. 10 6.
m s s
x m m v t s s
f. Determine the average acceleration from t = 2 s to t = 8.
2
4 ( 1 )
0.
8 2.
m m s s m s
v a t s s
g. What is the instantaneous velocity at t = 5 s? Explain.
In d. we found the average velocity for the interval of 2s to 8s. The midtime of this interval is
5s. Therefore the average and instantaneous are the same value of -2.
vel:
acc:
0m +
v v v v
a a a a
time (s)
position (m)
25
20
15
10
5
0 0510
Object D:
a. Give a written description of the motion. Object D is traveling in the negative direction at 4 m/s. At time t = 2s it begins to slow down and instantaneously stops 2s later. It then speeds up in the positive direction for 4s.
b. Sketch a motion map. Be sure to include both velocity and acceleration vectors.
c. Determine the displacement from t = 0s to t = 4 s. Using the area of the red section of the graph:
rectangle is 4 (2 ) 8 s m plus triangle
4 (2 )
4.
2
m
s s m = −12.
d. Determine the displacement from t = 4 s to t = 8 s. Using the area of the green section of the graph:
Triangle:
8 (4 )
16.
2
m s s m
e. Determine the displacement from t = 2 s to t = 6 s. By inspection one can see that the triangle in the negative section has the same area as the triangle in the positive section. Therefore the displacement is zero,
f. Determine the object’s acceleration at t =4s.
2
8 ( 4 ) 2. 8 2.
m m s s m s
v a t s s
g. Sketch a possible x-t graph for the motion of the object. Explain why your graph is only one of many possible graphs. We have no idea where the initial position for the trip is.
v (m/s) t (s)
0
2
4
6
8
-
-
-
-
2 4 6
vel:
acc:
0m +
v v v v start v v v v end
a
a a a a a a a a
x (m) t (s)
Accelerated Motion Worksheet Answers
Course: General Physics (PHYS 1120)
University: University of Nebraska at Omaha
