Active Learning: One Dimensional Kinematics
rev. 5/12
I Displacement and velocity
1. An object is moving to the right with constant velocity. Draw a sketch showing the position of
the object at 5 equally spaced times. (e.g. at t = 0, 1, 2, 3, 4 seconds)
2. A motorist traveling along the interstate looks at her watch just as she passes mile marker 82.
It=s 8:32. She then notes the time she passes several other mile markers: marker 104 at 8:50,
marker 131 at 9:35, and marker 156 at 9:55.
A. What was here speed between 8:32 and 8:50? (convert to mph)
B. What was her average speed for the full time interval (convert to mph)?
C. Her destination is at mile marker 240. What time will she arrive if she is able to maintain the
same average speed?
3. A motorist travels 65 mph for 35 miles and then runs into road construction so she has to slow
down to 25 mph for the next 5 miles.
A. What was the total time of the trip?
B. What was her average speed?
II Acceleration
1. An object is traveling to the left and slowing down.
A. Is the velocity positive or negative? Is the acceleration + or -?
B. Draw a sketch showing the object’s position at 5 equally spaced times (e.g. 0,1,2,3,4, s).
Active Learning: One Dimensional Kinematics
C. Describe the motion (direction of travel and speeding up/slowing down) for each of the
following:
1. +v, +a
2. +v, -a
3. –v, +a
4. –v, -a
2. Describe a real-life scenario where the following motions occur:
A. An object speeds up with decreasing magnitude of acceleration
B. An object slows down with increasing magnitude of acceleration
3. Rank the following according to the magnitude of the acceleration (largest to smallest)?
a. A particle speeding up from rest to 36 m/s in 6 s
b. A particle speeding up from 100 m/s to 200 m/s in 20 s
c. A particle coming to a stop from 8 m/s in 1 second
d. A particle speeding up from 50 m/s to 150 m/s in 10 s
e. A particle slowing from 250 m/s to 210 m/s in 20 s
Active Learning: One Dimensional Kinematics
4. The graph of x vs. t below represents the position of an object traveling along the x axis (right is
positive, left is negative).
A. Describe the motion in words.
B. Sketch a graph of velocity vs. time
C. Determine if the accelerations at the following times are positive, negative, or zero: t = 5, 30,
60, and 90 seconds.
6
5
x-position (m)
4
3
2
1
0
-1 0
10
20
30
40
50
60
70
80
90
100
-2
tim e (s)
III Constant Acceleration
1. You throw a ball straight up. What is the acceleration (magnitude and direction)? Air
resistance is negligible.
A. On the way up (after you release it)?
B. On the way down (before you catch it)?
C. Right at the top of flight?
D. How does the change of velocity in the first second after it leaves your hand compare to the
change in velocity in the first second after it reaches the peak?
Active Learning: One Dimensional Kinematics
2. You throw a ball straight up with an initial velocity of 12 m/s. Air resistance is negligible.
A. How high does it go before it starts back down (above your hand)?
B. How long does it take to reach the maximum height?
C. The ball lands two meters below the height from which it was thrown. How fast was it
traveling when it hit the ground?
D. How long was the ball in the air (from release to ground)?
3. Ball A is dropped from a window 10 m above the ground at the same time as ball B is launched
upward from ground level at 8 m/s.
A. Where do they meet?
B. Is ball B going up or down when the two balls meet?
Active Learning: One Dimensional Kinematics
IV Variable Acceleration
1. Sketch graphs of x vs. t for each of the following accelerations:
A. a = 0
B. a = constant positive value
C. a = increasing positive value
2. A particle initially traveling at +30 m/s accelerates from x = 0 at rest at t = 0 with variable
acceleration 𝑎 = 2.4√𝑡 m/s2. What are the velocity and position at t = 10 s?
3. A particle starts at rest from the origin with v = 16 - 4t4 m/s.
A. What is x(t)?
B. What are the velocity and acceleration when the particle returns to the origin?