Name
Period
Date
AP Physics
Motion in One Dimension Worksheet 3
1. The graph to the right pertains to an armadillo
that scampers left and right.
a. When if ever is the armadillo to the left of
the origin? How do you know?

x
1
2
3
4
5
6
7
b. When if ever is its velocity negative,
positive, or zero? How do you know?
2. How far does the runner whose velocity vs. time graph is shown below travel in
16 s ?
 s

vm
8
4
0
4
8
12
16
t s 
t
Motion in One Dimension – WS 3
page 2


2
3. A particle’s position is given by x  4  12t  3t (where t is in seconds and x is in
meters).
a. What is its velocity at t  1 s ?

b. Is it moving toward increasing or decreasing x just then? How do you know?
c. What is its speed just then?
d. Is the speed larger or smaller at later times? How do you know?
e. Is there ever an instant when the velocity is zero? When?
f. Is there a time after t  3 s when the particle is moving to the left? How do you
know?
Motion in One Dimension – WS 3
page 3

4. The position of an object moving in a straight line is given by x  3t  4t  t ,

where x is in meters and t in seconds.
a. What is the position of the object at t  1.0 s, 2.0 s, 3.0 s, and 4.0 s ?
2
3
b. What is the object’s displacement between t  0 s and t  4.0 s ?
c. What is the object’s average velocity between t  2.0 s and t  4.0 s ?

d. Graph the x vs. t for 0 s  t  4.0 s and indicate how the answer for (c) can be
found on the graph.

x m 
12
10
8
6
4
2
t s 
1
-2
2
3
4
Motion in One Dimension – WS 3
5. A particle had a velocity of 18 m
page 4
s
and 2.4 s later its velocity was 30 m
s
in the
opposite direction. What was the magnitude of the average acceleration of the
particle during this 2.4 s interval?


6. A particle moves along the x axis according to the function x  5.0 t  2.0 t , where

x is in meters and t in seconds.
a. Calculate the average velocity of the particle during the first 3.0 s of its motion.
2
b. Calculate the instantaneous velocity and the instantaneous acceleration of the
particle at t  3.0 s .

c. Graph the x vs. t and indicate on the
graph how the average velocity from (a)
and the instantaneous velocities from (b)
can be obtained.

x m 
t s 

d. Graph the v vs. t and indicate on the
graph how the instantaneous acceleration
from (b) can be obtained.
 s

v m
t s 
Motion in One Dimension – WS 3
page 5


3
7. The position of a particle is given by x  20. t  5.0t , where x is in meters and t in
seconds.
a. When, if ever, is the particle’s velocity zero?
b. When is its acceleration zero?
c. When is its acceleration negative? Positive?



d. Graph x t  , v t  , and a t  .
 s
 s

x m 

v m
t s 

a m
t s 
2
t s 
Motion in One Dimension – WS 3
page 6


8. The position of a particle is given by x  2.0t , where x is in meters and t in
seconds.
a. Calculate the instantaneous velocity and the instantaneous acceleration of the
particle at t  1.0 s and t  2.0 s .
3
b. Calculate the average velocity and the average acceleration of the particle
between t  1.0 s to t  2.0 s .


c. Graph the x vs. t and the v vs. t and indicate on the graphs how the answers
from (a) and (b) can be obtained.
 s

v m

x m 
t s 
t s 