In Exercise 1, use a standard rectangular Cartesian coordinate system.
Let time t be represented along the horizontal axis.
Assume all accelerations and decelerations are constant.
1.
Consider a PSA initially at rest in the beginning of the left-hand end of a long ISS corridor.
Assume xo = 0 on the left end of the ISS corridor.
At t0 an astronaut requests an emergency video conference with ground control and the PSA
uniformly accelerates to the right for several seconds > t3.
A.
For the PSA’s motion described above,
In the first diagram, sketch the graph of acceleration vs. time.
In the second diagram, sketch the graph of velocity vs. time, and
In the third diagram sketch of displacement vs. time.
a
v
x
t
t
t1
B.
t3
t1
t2
t3
t1
t2
t3
For the PSA’s motion described above, draw vectors representing Acceleration, Velocity and
Displacement at the four times listed below.
ao
C.
t2
t
a1
a2
a3
vo
v1
v2
xo
v3
x1
x2
x3
In each case, circle the answer that best describes the situation.
When t1 < t < t3 Acceleration is:
constant
changing
zero
positive
negative
When t1 < t < t3 Velocity is:
constant
changing
zero
positive
negative
When t1 < t < t3 Displacement is: constant
changing
zero
positive
negative
In Exercise 2, use a standard rectangular Cartesian coordinate system.
Let time t be represented along the horizontal axis.
Assume all accelerations and decelerations are constant.
2.
Ground control is using a PSA’s video camera to survey the progress of several dozen biology
experiments.
At to the PSA is initially moving at a constant speed in a straight line from left to right.
At t2 ground control directs the PSA to accelerate to a greater speed in the same direction for
several seconds > t3.
A.
For the PSA’s motion described above,
In the first diagram, sketch the graph of acceleration vs. time.
In the second diagram, sketch the graph of velocity vs. time, and
In the third diagram sketch of displacement vs. time.
a
v
x
t
t
t1
B.
t3
t1
t2
t
t3
t1
t2
t3
For the PSA’s motion described above, draw vectors representing Acceleration, Velocity and
Displacement at the four times listed below.
ao
C.
t2
a1
a2
a3
vo
v1
v2
xo
v3
x1
x2
x3
In each case, circle the answer that best describes the situation.
When to < t < t2 Acceleration is:
constant
changing
zero
positive
negative
When to < t < t2 Velocity is:
constant
changing
zero
positive
negative
When t2 < t < t3 Displacement is: constant
changing
zero
positive
negative
In Exercise 3, use a standard rectangular Cartesian coordinate system.
Let time t be represented along the horizontal axis.
Assume all accelerations and decelerations are constant.
3.
Consider a PSA initially moving at constant velocity from left to right in a long ISS corridor.
At to an astronaut commands the PSA to decelerate.
At t1.5 the PSA stops moving to the right and begins accelerating to the left.
At t3 the PSA has reached the same constant speed it started with, only now moving from right
to left.
A.
For the PSA’s motion described above,
In the first diagram, sketch the graph of acceleration vs. time.
In the second diagram, sketch the graph of velocity vs. time, and
In the third diagram sketch of displacement vs. time.
a
v
x
t
t
t1
B.
t3
t1
t2
t
t3
t1
t2
t3
For the PSA’s motion described above, draw vectors representing Acceleration, Velocity and
Displacement at the four times listed below.
ao
C.
t2
a1
a2
a3
vo
v1
v2
xo
v3
x1
x2
x3
In each case, circle the answer that best describes the situation.
When t0 < t < t1.5 acceleration is:
constant
changing
zero
positive
negative
When t1.5 < t < t3 velocity is:
constant
changing
zero
positive
negative
When t0 < t < t1.5 displacement is: constant
changing
zero
positive
negative
In Exercise 4, use a standard rectangular Cartesian coordinate system.
Let time t be represented along the horizontal axis.
Assume all accelerations and decelerations are constant.
4. Consider a PSA moving at top speed in a straight line from left to right.
Suddenly, an astronaut floats down and stops directly in front of the PSA.
Between t0 and t1 the PSA quickly decelerates to rest in order to avoid hitting the astronaut.
Between t1 and t2 the PSA stops and remains at rest as the astronaut moves out of the way.
At t2 the PSA begins to accelerate from left to right until reaching it’s top speed.
A.
For the PSA’s motion described above,
In the first diagram, sketch the graph of acceleration vs. time.
In the second diagram, sketch the graph of velocity vs. time, and
In the third diagram sketch of displacement vs. time.
a
v
x
t
t
t1
B.
t3
t1
t2
t
t3
t1
t2
t3
For the PSA’s motion described above, draw vectors representing Acceleration, Velocity and
Displacement at the four times listed below.
ao
C.
t2
a1
a2
a3
vo
v1
v2
xo
v3
x1
x2
x3
In each case, circle the answer that best describes the situation.
When t0 < t < t1 acceleration is:
constant
changing
zero
positive
negative
When t1 < t < t2 velocity is:
constant
changing
zero
positive
negative
When t2 < t < t3 displacement is: constant
changing
zero
positive
negative
In Exercise 5, use a standard rectangular Cartesian coordinate system.
Let time t be represented along the horizontal axis.
Assume all accelerations and decelerations are constant.
5. Consider a PSA initially at rest.
At t0 the PSA accelerates from left to right towards the center of a long ISS corridor.
At t1 the PSA stops accelerating and continues moving at a constant speed until t2.
At t2 the PSA decelerates and comes to rest at t3.
A.
For the PSA’s motion described above,
In the first diagram, sketch the graph of acceleration vs. time.
In the second diagram, sketch the graph of velocity vs. time, and
In the third diagram sketch of displacement vs. time.
a
v
x
t
t
t1
B.
t3
t1
t2
t
t3
t1
t2
t3
For the PSA’s motion described above, draw vectors representing Acceleration, Velocity and
Displacement at the four times listed below.
ao
C.
t2
a1
a2
a3
vo
v1
v2
xo
v3
x1
x2
x3
In each case, circle the answer that best describes the situation.
When t1 < t < t2 acceleration is:
constant
changing
zero
positive
negative
When t2 < t < t3 velocity is:
constant
changing
zero
positive
negative
When t0 < t < t3 displacement is:
constant
changing
zero
positive
negative
Vertical Position vs. Time of a
14
12
P
O
10
8
6
S
I
4
2
T
0
I
-2
O
-4
N
-6
(m)
-8
0
2
4
6
8
10
12
14
16
18
20
22
-10
-12
Time (s)
Consider the above Displacement vs. Time graph above. It represents the vertical displacement
of a squirrel as it climbs up and down a tree. The squirrel starts at Y = 0 m which represents
the lowest branch on the tree.
1. During which times is the Squirrel moving:
a) towards the top of the tree? (0s < t < 2s), (4s < t < 6s), (13s < t < 16s), (18s < t < 20s)
b) away from the top of the tree? (6s < t < 12s), (16s < t < 18s)
c) not moving vertically? (2s < t < 4s), (12s < t < 13s), (20s < t < 22s)
2. Find the average velocity for:
a) the time interval between 3 ≤ t ≤ 5 seconds.
v3-5s = + 3 m/s
b) the time interval between 10 ≤ t ≤ 13 seconds.
v10-13s = - 8/3 m/s
c) the time interval between 0 ≤ t ≤ 20 seconds.
V0-20s = 0 m/s
3. How many times does the squirrel return to the lowest branch on the tree? Four Times
4. Find the average velocity between t=18 to t=20 seconds. Vavg = + 5 m/s
5. Predict the squirrel’s velocity at t = 12.5 s.
V12.5 = 0 m/s
6. When the displacement is negative, what does that mean in terms of the squirrels position on the
tree with respect to the lowest branch? The squirrel is below the lowest branch.
7. At what time(s) does the Squirrel change direction? t = 6s, t = 13s, t = 16s, t = 18s
8. What is the Squirrel’s maximum displacement from the lowest branch ? + 12 m
9. When is the Squirrel speeding up? t = 4s, t = 6s, t = 10s, t = 16s, t = 18s
10. When is the Squirrel slowing down? t = 2s, (4s < t < 6s), (10s < t < 13s), (14s < t < 16s), t = 18s
11. What is the Squirrel’s acceleration between t=6 and t=10 seconds? 0 m/s2
Kinematics Graphs
Given either an acceleration, velocity or displacement graph, sketch graphs of the missing two.
Example: Given a constant positive velocity… sketch graphs of acceleration and displacement.
a
v
t1
t2
t3
x
t1
t2
t3
t1
t2
t3
t1
t2
t3
t1
t2
t3
t1
t2
t3
a.
a
v
t1
t2
t3
x
t1
t2
t3
b.
a
v
t1
t2
t3
x
t1
t2
t3
c.
a
v
t1
t2
t3
x
t1
t2
t3
d.
a
v
t1
t2
t3
x
t1
t2
t3
t1
t2
t3
t1
t2
t3
t1
t2
t3
t1
t2
t3
e.
a
v
t1
t2
t3
x
t1
t2
t3
f.
a
v
t1
t2
t3
x
t1
t2
t3
g.
a
v
t1
t2
t3
x
t1
t2
t3
In-Class Problems – 1 Dimensional Kinematics
Neglect air resistance unless otherwise specified.
1. The position of a model radio controlled car racing down a straight track was observed at
various times and the results are summarized in the table below.
x (m)
t (s)
0
0
2.3
1.0
9.2
2.0
20.7
3.0
36.8
4.0
a. Find the average velocity of the car for the 1st second.
b. Find the average velocity of the car for the last 3 seconds.
c. Find the average velocity of the car for entire period of time.
d. Find the average speed of the car for the entire period of
time.
57.5
5.0
2. A LAHS swimmer swims the length of a 50.0m pool in 20.0s and makes the return trip to
the starting position in 22.5s.
A.
B.
C.
D.
Predict the average velocity in the first half of the swim.
Predict the average velocity in the last half of the swim.
Predict the average velocity in the round trip.
Predict the average speed in the round trip.
3.
A very light cheerleader is thrown straight up in the air by her
colleagues. Her initial velocity upon losing contact with the throwers
is 14.7 m/s at t=0. At t=1.50 s she reaches the apex of her vertical
trajectory where her velocity 0 m/s.
A.
Predict the cheerleader’s average acceleration during this 1.50 s interval? What is the
significance of the negative sign of your answer?
If the cheerleader continues to accelerate at the same rate, predict the cheerleader’s
final velocity just before she’s caught at the same level she was thrown?
Graph the cheerleader’s displacement, velocity and acceleration vs. time.
B.
C.
4.
Consider a cliff diver falling from rest from the top of a 125 m tall cliff
edge.
A.
Predict the time it takes the diver to reach the water 125 m below the
cliff’s edge.
B.
Predict the velocity of the cliff diver just before she reaches the water.
C.
Predict the average velocity of the cliff diver during her freefall.
D.
Graph the cliff diver’s displacement, velocity and acceleration vs. time.
5.
Consider a furniture mover trying to save time by launching boxes upward
from the ground level to another mover leaning out a 3rd story window. If the
second mover’s hands are 11.5 m above the ground…
A.
Predict the initial velocity a box must have such that the 2nd mover can reach
out and grab the box when it’s at its apex.
B.
Predict the time for the box to reach its apex.
C.
If the 2nd mover doesn’t catch the box, predict its velocity just before it hits the ground.
D.
Graph the box’s displacement, velocity and acceleration vs. time.
7.
Consider a Sprint car driver racing at a constant speed around a circular track with a
of 85.0 m.
A.
Calculate her average speed if she completes one quarter of a lap in 8.0 s.
B.
Calculate her average velocity for the same 8.0 s quarter turn.
C.
Calculate her average velocity for a complete revolution.
radius
8.
Consider Carla driving along a straight stretch of roadway at a constant velocity of 35
m/s. At the exact same time she passes a police car it begins to uniformly accelerate
after her, from rest, at 4.5 m/s2.
A.
B.
C.
D.
How much time passes before the police car catches up to Carla?
How far has Carla driven before the police car passes her?
How far has the police car driven before passing Carla?
Graph Carla’s and the police officer’s displacement vs. time on the same graph. What does
the intersection point represent?
Graph Carla’s and the police officer’s velocity vs. time on the same graph. What does the
intersection point represent? How is the area under Carla’s velocity vs. time graph
related to the area under the officer’s velocity vs. time graph?
E.