Motion Test Review
Name: _________________________________Date: _________Period__
Practice problems for speed and velocity. The formula for speed is distance / time = speed
Velocity is calculated the same way but you need to include the direction when you are
asked for a velocity. There are three types of speed math problem.
Solve for speed, solve for distance and solve for time.
Solve for speed and velocity.
1. The train traveled 500 kilometers north to Odessa in 2 hours. What is the train’s
speed? What is its velocity?
2. Ann walked 1.5 miles south to her house in 0.5 hours. What is Ann’s speed? What is
Ann’s velocity?
3. Jeremiah ran around the track at the YMCA for 2 hours. When he was done he figured
that he had traveled 20 kilometers. What was his speed? What was his velocity?
4. The race car was moving for 3.7 hours and during that time moved 500 miles east. What
is the speed? What is the velocity?
Solve for distance.
6. Mike is driving west on I-10 for 1.5 hours at a speed of 70 miles per hour. What is his
distance?
Solve for time.
7. If you are traveling at 75 km/h how long will it take to travel 32 km?
ACCELERATION PRACTICE PROBLEMS
You can use a calculator
SHORT ANSWER
1. Does the speedometer of a car read average speed or instantaneous speed? How do you
know?
2. If the speedometer of your car reads a constant speed of 40km/hr, can you say 100%
for sure that the car has a constant velocity? Explain your answer.
3. What two controls on a car cause a change in speed?
4. What control causes a change in velocity?
5. What is the acceleration of a car that travels in a straight line at a constant speed?
6. Describe a situation in which you can accelerate even though your speed doesn’t change.
CALCULATIONS
7. A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts down the
slope, its speed is 4 m/s. But 3 seconds later, at the bottom of the slope, its speed is 22
m/s. What is its average acceleration?
8. A cyclist accelerates from 0 m/s to 8 m/s in 3 seconds. What is his acceleration? Is this
acceleration higher than that of a car which accelerates from 0 to 30 m/s in 8 seconds?
10. A lizard accelerates from 2 m/s to 10 m/s in 4 seconds. What is the lizard’s average
acceleration?
11. A runner covers the last straight stretch of a race in 4 s. During that time, he speeds up
from 5 m/s to 9 m/s. What is the runner’s acceleration in this part of the race?
12. You are traveling in a car that is moving at a velocity of 20 m/s. Suddenly, a car 10 meters
in front of you slams on its brakes. At that moment, you also slam on your brakes and slow
to 5 m/s. Calculate the acceleration if it took 2 seconds to slow your car down.
13. A ball is dropped from the top of a building. After 2 seconds, its velocity is measured to
be 19.6 m/s. Calculate the acceleration for the dropped ball.
Acceleration is the rate of change in the speed of an object. To determine the rate of
acceleration, you use the formula below. The units for acceleration are meters per second
per second or m/s2.
A positive value for acceleration shows speeding up, and negative value for acceleration
shows slowing down. Slowing down is also called deceleration.
The acceleration formula can be rearranged to solve for other variables such as final
speed (v2) and time (t).
EXAMPLES
16. A skater increases her velocity from 2.0 m/s to 10.0 m/s in 3.0 seconds. What is the
skater’s acceleration?
Looking for
Acceleration of the skater
Given
Beginning speed = 2.0 m/s
Final speed = 10.0 m/s
Change in time = 3 seconds
Relationship
Solution
The acceleration of the skater is 2.7 meters per
second per second.
17. A car accelerates at a rate of 3.0 m/s2. If its original speed is 8.0 m/s, how many
seconds will it take the car to reach a final speed of 25.0 m/s?
Looking for
Solution
The time to reach the final speed.
Given
Beginning speed = 8.0 m/s; Final speed
= 25.0 m/s
Acceleration = 3.0 m/s2
`
The time for the car to reach its final speed is
5.7 seconds.
Relationship
19. A parachute on a racing dragster opens and changes the speed of the car from 85 m/s
to 45 m/s in a period of 4.5 seconds. What is the acceleration of the dragster?
20. The table below includes data for a ball rolling down a hill. Fill in the missing data values
in the table and determine the acceleration of the rolling ball.
Time (seconds)
Speed (km/h)
0 (start)
0 (start)
2
3
6
9
8
10
15
Acceleration = ___________________________
21. A car traveling at a speed of 30.0 m/s encounters an emergency and comes to a
complete stop. How much time will it take for the car to stop if it decelerates at -4.0
m/s2?
25. A helicopter’s speed increases from 25 m/s to 60 m/s in 5 seconds. What is the
acceleration of this helicopter?
24. As she climbs a hill, a cyclist slows down from 25 mi/hr to 6 mi/hr in 10 seconds. What
is her deceleration?
28. A cyclist accelerates at a rate of 7.0 m/s2. How long will it take the cyclist to reach a
speed of 18 m/s?
30. Define acceleration
31. Write the equation for acceleration
32. What is the acceleration due to gravity?
33. A Porsche 911 can go from 0 to 60 mph in 3.4 seconds.
What is its acceleration? (your answer will be in
miles/hour/second)
34. If you are riding your bike and hit a curb, you would stop suddenly.
say that you were going 25 m/s when you hit the curb and it
took you only .75 seconds to stop after hitting the curb.
What was your acceleration?
Lets
35. If you were in a car going 275 m/s and a deer runs out in front of you. You
slammed on the brakes to avoid hitting the deer. It took 2.5 seconds to slow to
83 m/s. What was your acceleration?
36. What is free fall motion?
37. How do you calculate how fast an object falls?
38. What is the formula for acceleration?
Simple Free Fall Problems
Problem 1 only
https://www.youtube.com/watch?v=BA3VGbpr_bw
In Free Fall – MOTION is IN THE VERTICALONLY or y direction ONLY!
If a person DROPS an object, not THROWS, the initial velocity of the object is always
0.0 m/s DOWNWARD – velocity is a VECTOR so it must have DIRECTION!
EVERY SECOND of FREE FALL the velocity changes by 10 m/s.
On the Earth:
39. A bowling ball falls freely (near the surface of the Earth) from rest. How far does it
fall in 4 seconds, and how fast will it be going at that time?
The ball's average speed for the first 4 seconds is the average of 0 m/s and 40 m/s, its
starting and ending speeds, and distance = average speed times time.
So the object will have fallen 80 meters, and its speed will be 40 m/s.
Solution 3 - An Algebraic Approach
Since the ball started from rest:
v = gt = (10 m/s2)(4s) = 40 m/s
So the object will have fallen 80 meters, and its speed will be 40 m/s.
40.
Staying still
Constant
Speed up
Slow down
Motion Graphs Videos
https://www.youtube.com/watch?v=lTE83sP7lQg
Use this link to check your understanding of motion graphs
http://www.proprofs.com/quiz-school/story.php?title=graphing-motion-quiz
Mike walks 11 km N then 11 km E. What is Mike’s displacement?
The result of adding 11 km, north plus 11 km, east is a vector with a
magnitude of 15.6 km.
Free Fall & Throwing Objects into the Air
THROW-UP PROBLEM EXAMPLE
2. How long does it take a ball to reach the ground 7.0 m below, if it is thrown straight up with
an initial speed of 2.00 m/s?
Now we can see we need a relationship between d, a, vi, and t
d = (0.5)at2
(7.0 m) = (-2.00)t + (0.5)(9.8)t2
t = {1.42}