Physics R Date: __________________
Kinematics 2: Motion Graphs & Free Fall
Every morning Tom walks along a straight road from his home to a bus stop, a distance of 160 meters.
The graph shows his journey on one particular day.
Describe what may have happened. You should include details like how fast he walked.
1
1 2
2.
3.
3 4
4.
5.
5 6
6.
-8
-6
-4
-2
0
2
4
6
8
0 2 4 6 8 10 12 14
Dis
pla
cem
en
t (m
)
Time (s)
How do you calculate the slope of a line?
What would the slope of a distance vs time graph represent?
What would the slope of a displacement vs time graph represent?
What would the slope of a velocity vs time graph represent?
You could memorize all of these, or you could just remember that slope=
Position (or distance or displacement) vs time graph
1. During which intervals is the
object stopped?
2. During which interval is the
object’s position changing the
fastest?
3. What is the object’s velocity
during this time?
4. During which interval does the object
have the highest velocity?
5. What is its velocity during this time?
6. What is the velocity from 8-9 s?
Position vs Time
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8
Time (s)
Dis
pla
cem
en
t (m
)
Velocity vs time graph
Tom’s older brother Mot just turned 17 and his parents bought him a car. To make sure he doesn’t
speed, a velocity-meter was installed in the car to record what the speedometer says (along with
direction, forward or reverse). The graph shows his journey to school on one particular day.
0
5
10
15
20
25
30
35
0 10 20 30 40 50 60 70 80 90 100 110 120
Ve
loci
ty (
m/s
)
Time in seconds
Describe what may have happened. You should include details like how hard he stepped on the gas or
brakes.
-4
-2
0
2
4
6
0 2 4 6 8 10Ve
loc
ity (
m/s
)
Time (s)
Under each of the graphs below, describe, in one or two words, the motion of each object.
Velocity (or speed) vs Time Graph
7. What is the acceleration from
0-4 seconds?
8. What is the displacement from
2-4 seconds?
9. What is the velocity from
9-10 seconds?
10. When is the velocity zero?
6
What does speeding up look like
What does slowing down look like?
Graphing Practice Sketch displacement vs time and velocity vs time for each
11. A ball sits motionless on a table at a position 3 meters to the right of the origin.
12. A man starts at a location 5 meters north of his house. He walks away from his house with a
constant speed of 1 meter per second.
7
13. A boy starts 6 meters west of his house. He runs toward his house with a constant speed of 10
meters per second and continues running by his house.
14. A woman leaves her house moving north. Starting from rest, she accelerates at a rate of 1 m/s2 as
she travels away from the house.
15. Write a description for the following motion graph, and fill in the missing motion graph.
a.
b.
c.
8
-4
-2
0
2
4
6
8
0 2 4 6 8 10 12 14
Ve
loc
ity (
m/s
)
Time (s)
Car A solid, Car B dashed
16. What is the acceleration of car
A from 0-4 seconds?
17. What distance does car A cover
from 0-7 seconds?
18. What is the acceleration of car
B from 0-7 seconds?
19. What is the acceleration for car B from 7-10 seconds?
20. What distance does car B travel from 4-7 seconds?
21. What is the velocity of car B at 5 seconds?
22. What is the displacement of car A over the entire 14 seconds?
23. The graph below represents the relationship between
speed and time for an object moving along a straight
line.
What is the total distance traveled by the object during
the first 4 seconds?
1. 5 m
2. 20 m
3. 40 m
4. 80 m
Use the following graph for #43-44
24. What is the acceleration of the car at t=5.0 seconds?
1. 0.0 m/s2
2. 2.0 m/s2
3. 2.5 m/s2
4. 10 m/s2
25. What is the total distance traveled by the car during
this 6-second interval?
1. 10 m
2. 20 m
3. 40 m
4. 60 m
9
Motion Graph Practice The most important thing to do with any motion graph is to read the axes. If you don’t know what type
of graph you’re looking at, you will not know what to do to answer the questions involved.
Slope from displacement -> Slope from velocity ->
DVA Area under velocity ->
26. a. What type of graph is this?
b. What is the object doing from 2-5 seconds?
c. What is the displacement from 2-5 seconds?
d. What is the velocity at t=1 second?
e. What is the acceleration from 2-5 seconds?
27. a. What type of graph is this?
b. What is the object doing from 0-3s?
c. What is the velocity from 0-3s?
d. What is the displacement from 0-3s?
28. a. What is the velocity at t=3 seconds?
b. What is the velocity at t=1 second?
c. What is the velocity at t=5 seconds?
d. What is the object doing from 4-6 seconds?
10
29. a. What is the velocity at t=3 seconds?
b. What is the acceleration from 4-6 seconds?
c. What is the displacement from 0-2 seconds?
d. What is the displacement over the entire 6 seconds?
e. What is the acceleration at t=1 second?
30. a. What is the speed of this object at t=3 seconds?
b. What is the displacement over the entire 6 seconds?
c. What is the speed of this object from 4-6 seconds?
31. a. What is the object doing from 0-2 seconds?
b. What is the object doing from 4-6 seconds?
c. Calculate the acceleration of the object at t=2 s.
d. Calculate the acceleration of the object at t=5 s.
e. Calculate the total displacement from 0-2 s
f. What is the velocity of the object at t=2 s.
11
Free-Fall What happens to an object as it falls?
‘g’ is different on different planets
Earth Moon Jupiter
Why do some objects fall slower than others?
What if objects were dropped in a vacuum?
What happens when I drop an object?
Time (s) Velocity (m/s) Displacement (m) Acceleration (m/s2)
t = 0
t = 1
t = 2
t = 3
t = 4
When I drop an object, it starts:
Motion graph for a dropped object in free fall
Displacement vs. Time Velocity vs. Time Accel vs. Time
12
-12
-10
-8
-6
-4
-2
0
0 1 2 3 4 5 6
Time (s)
Velo
cit
y (
m/s
)
(Ignore air resistance for all problems)
32. I drop a penny off the Empire State Building, which is 448.7m tall. How much time will it take
until the penny hits an unsuspecting pedestrian?
What is the initial velocity of the penny?
What is the acceleration of the penny?
What is the displacement of the penny (start-to-finish)?
What is the question asking for?
33. Mr. Vigneaux decides to jump out of an airplane from an altitude of 4000 m. How fast is he going
when his parachute (hopefully) opens at an altitude of 1000 m?
34. An astronaut lands on Planet X and drops a marble from a height of 2 m. The marble hits the
ground 3.2 seconds later. What is the acceleration due to gravity on Planet X, where the astronaut loses
his marbles?
35. A helicopter drops a “care package” above a foreign country. The parachute on the “care package”
is designed to open when the “care package” is traveling at 75 m/s. How much time will elapse between
the “care package” dropping and the parachute opening?
36. The velocity-time graph shows the
velocity of an object dropped on the moon
of Planet X. What is the acceleration due
to gravity on this moon?
13
37. a) Mr. Vigneaux drops an egg off the school building (11m tall) onto a student who failed the last
exam, but he has bad aim and he misses. How long until the egg hits the ground?
b) How fast is the egg moving when it hits the ground?
When an object is dropped, what is the initial velocity of the object?
What if the object is thrown downward?
What if the object is thrown upward?
38. A cat is thrown downward off a 125 m tall building with a speed of 10 m/s.
a) What is the initial velocity of the cat?
b) What is the acceleration of the cat?
c) How fast is the cat going the instant it hits the ground?
39. A cannon fires a shot directly upward at 50 m/s.
a) What is the initial velocity of the cannonball?
b) What is the acceleration of the cannonball?
c) What is the speed of the cannonball at the instant it hits its highest point?
(This question is important!!!)
d) Create a motion graph that shows the ball going up and down. Circle the instant it hits the peak
Displacement vs. Time Velocity vs. Time Accel vs. Time
e) How much time does it take to reach this peak?
f) How much total time does the cannonball spend in the air?
14
40. A coin is tossed vertically upward (no air resistance). (a) Describe what happens to the velocity over
the entire course of its path in the air (b) does the acceleration increase, decrease or remain constant
while in the air?
41. A pebble is dropped down a well and hits the water 1.25 sec later. Determine the distance from the
top of the well to the water below.
42. A ball is thrown vertically upward, what are the velocity and acceleration at the peak where it
reaches its maximum altitude.
43. A cannon ball is launched directly upwards at an initial speed of 17.5 m/s. (a) What maximum
height does it reach and (b) how long is it in the air for over its whole up and down trip.
44. A student throws a baseball vertically upward and then catches it. If vertically upward is considered
to be the positive direction, which graph best represents the relationship between velocity and time for
the baseball? [Neglect friction.]
45. An insect jumps straight up into the air and you are able to record its maximum height of 0.8 meters
before you scream and wave your arms in the air. Calculate the initial velocity of the insect the moment
it jumps off the ground.
15
Objects Launched Upwards A cannon fires a projectile directly upwards with an initial velocity of 40 m/s.
Round g to 10 m/s2 to make the math easier.
Fill in the displacement (use d = vit + ½ a t2) for each position shown below
Fill in the velocity (use vf = vi + at) for each position shown below
Fill in the acceleration for each position shown below
Notice that free-fall is a mirror image up and down! Time up = time down, initial velocity at the ground
= final velocity when it returns to the ground (but don’t forget – final velocity at the peak = 0)
16
46. A jellyfish is launched out of the ocean with an initial velocity of 19.6 m/s. Two seconds later it
reaches its maximum height. (a) How much total time does the jellyfish spend in the air?
(b) With what speed will the jellyfish have when it returns to the ocean?
47. An archer launches an arrow straight upward. (a) How fast does he have to shoot the arrow to hit a
pigeon flying directly overhead at a height of 82 meters?
(b) How much total time will the arrow spend in the air?
48. A child shoots a spitball directly upwards. It hits goes straight up and then down and lands on his
forehead 0.8 seconds later. What maximum height did the spitball reach?
49. Muggsy Bogues was 5 foot 3 inches tall (1.6 m) and could slam dunk a basketball. (a)How high did
he have to be as high as the rim (3 meters above the ground)?
(b) What initial velocity did he need to reach this height?
(c) How much total time did he spend in the air?
50. Wile E Coyote accidentally catapults himself up with a speed of 46 m/s. (a) What maximum height
does he reach?
(b) What is his final velocity at the peak of his voyage?
(c) How much total time does he spend in the air?
(d) What is his final velocity when he returns to the ground?
51. A tauntaun on planet Hoth jumps upward with an initial velocity of 12 m/s. It returns to the ground
4.5 seconds later. (a) Calculate the acceleration due to gravity on planet Hoth.
(b) What final velocity will the tauntaun have when it returns to the ground?
(c) What maximum height will the tauntaun reach?
17
Review Checklist
Use equations to determine distance; displacement; speed; velocity; acceleration; or time.
1. How far does an object travel if it starts from rest and accelerates at a rate of 2.0 meters per second2
for 6.5 seconds?
2. What is the final speed of a cart that begins with a velocity of +3.0 meters per second if it accelerates
at a rate of +1.5 meters per second2 while traveling +25 meters?
3. At what rate does an object accelerate if it changes its speed from 3.0 meters per second to 5.0 meters
per second while traveling a distance of 4.0 meter?
4. How long does it take for an object to reach a velocity of 2.0 meters per second north if it begins
with a velocity of 8.0 meters per second south and accelerates north at a rate of 4.0 meters per second2?
5. A race car starting from rest accelerates uniformly at 4.9 m/s2. What is the car’s speed after it has
traveled 120 meters?
6. A car initially traveling at a speed of 16 meters per second accelerates uniformly at a rate of 2.9 m/s2
for 12 seconds. What distance does the car travel?
7. Jimmy accelerates his car from rest to 25 m/s over a distance of 100 meters. What is his average
speed over this time?
8. A train slows from 30 m/s to 20 m/s in 4 seconds. What is the magnitude of the average velocity of
the train during this time?
Interpret graphs of distance or displacement vs. time. Calculate speed/velocity from a
distance/displacement graph. Interpret graphs of speed or velocity vs. time. Calculate acceleration from
a speed/velocity graph. Calculate distance/displacement from a speed/velocity graph.
9. When is this object moving fastest? What is its speed during
this interval?
10. What is the speed of the object at t=8 s?
11. What is the speed of the object from 9-10 s?
12. During what intervals is the object not moving?
13. What is the speed of this object at t=3 seconds?
14. What is the speed of this object from 1-2 seconds?
15. When does the object have the highest speed?
What is it?
18
16. When is this object not moving?
17. What is the speed of the object from 1-4 seconds?
18. How much distance does the object travel from 0-4 seconds?
19. What is the acceleration of this object from 0-2 seconds?
20. What is the acceleration of this object from 2-3 seconds?
21. What is the displacement from 0-4 seconds?
22. When is the object not moving?
23. What is the acceleration of the object from 3-4 seconds?
24. What is the acceleration of the object from 4-5 seconds?
Explain the behavior of objects in free-fall (in the absence of air resistance.). Understand the terms
“dropped” and “maximum height”.
25. What speed will a ball reach if it falls from rest for 3.0 seconds?
26. How far will a dropped object have fallen after 2.0 seconds?
27. What maximum height will an object reach if it thrown directly upward with a speed of 15 meters
per second? How long will it take to reach this height?
28. What is the height of an object that is thrown upward with a speed of 20 meters per second 1.5
seconds after it is thrown?
29. An object is thrown directly upward with a speed of 25 meters per second. How long will it take to
come back to the position from which it was released?
19
30. How long does it take for an object that is dropped from the top of a 45 meter high building to reach
the ground?
31. An elephant drops a peanut, which hits the ground with a speed of 6 m/s. What is the average speed
of the peanut on its trip to the ground?
32. A marble launcher shoots a marble directly upwards. The marble reaches a height of 1.8 meters.
a. What is the initial velocity of the launched marble?
b. What is the acceleration of the marble at the peak?
c. The marble returns to the marble launcher. What speed does it have when it hits?
33. An angry bird shoots directly upwards from a slingshot with an initial velocity of 35 m/s.
a. How much time does it take the bird to reach the peak?
b. How much total time does the bird spend in the air?
c. With what speed is the angry bird moving when it returns to the ground?
The exam will be comprehensive. Go over the review checklist in Kinematics 1 and Physics Skills also.
20
Answers to Review Checklist
1. 42.3 m
2. 9.2 m/s
3. 2 m/s2
4. 2.5 s
5. 34.3 m/s
6. 401 m
7. 12.5 m/s
8. 25 m/s
9. 3-4 s, 3 m/s
10. 0 m/s
11. 2 m/s
12. 1-3, 4-5, 6-9 s
13. 0 m/s
14. 2 m/s
15. 7-8s, 5 m/s
16. 0s, 8-10s
17. 2 m/s
18. 7 m
19. 1 m/s/s
20. 0 m/s/s
21. 5 m
22. 0s, 4s, 8-10s
23. -2 m/s/s
24. -1 m/s/s
25. 29.4 m/s
26. 19.6 m
27. 11.5 m, 1.53 s
28. 19 m
29. 5.1 s
30. 3.03 s
31. 3 m/s
32. a. 5.9 m/s
b. -9.8 m/s2
c. -5.9 m/s
33. a. 3.6 s
b. 7.2 s
c. -35 m/s
