Unit 2 Motion Equations
1.
2.
Motion Equations
A race car accelerates from 0 m/s to 30.0 m/s with a
displacement of 45.0 m. What is the vehicle's
acceleration?
14. A bullet accelerates through a 0.11 m barrel for 0.005 s
as the gun is fired. With what acceleration does the
bullet experience in the barrel?
15. An airplane landing on the runway slows with an
A marble accelerates from rest at a constant rate and
acceleration of -11.5 m / s 2 . If the plane stops after
travels for a total displacement of 44 m in 20.0 s. What is
traveling 212 m down the runway, how fast was it
the final velocity of the marble?
traveling when it first touched ground?
3.
A curious kitten pushes a ball of yarn at rest with its
nose, displacing the ball of yarn 1.75 m in 2.00 s. What is
the acceleration of the ball of yarn?
16. A soccer ball is kicked and sent rolling at 22 m/s. How far
will it roll in order to come to a stop if it takes
9.2 seconds to stop?
4.
A sports car accelerates at a constant rate from rest to a
speed of 27.8 m/s in 8.00 s. What is the displacement of
the sports car in this time interval?
5.
17. An airplane landing on the runway slows with an
acceleration of -15 m / s 2 . If the plane stops after
traveling 400 m down the runway, how fast was it
traveling when it first touched ground?
A skate board starting from rest accelerates at a rate of
2.5 m / s 2 . How long will it take the skate board to attain 18. A tennis ball rolling across the floor at 2 m/s experiences
a speed of 8.31 m/s?
an acceleration of -0.5 m / s 2 . How far will the ball roll
before it stops?
A car starting from rest accelerates down the street.
How fast will the car be moving if it cover 200 m in 25 s? 19. A skateboard rider starts from rest and maintains a
6.
2
7.
An airplane needs to build up a speed of 92 m/s in order
to take off. If the runway is 400 m long, how much time
does the plane have to build up enough speed to get off
the ground?
8.
A car accelerates at a rate of 0.6 m / s 2 from rest for 5 s.
How far does it move in this time?
9.
A bullet accelerates through a 1.1 m barrel for 0.02 s as
the gun is fired. With what velocity does the bullet leave
the barrel?
constant acceleration of 0.50 m/s for 8.4 s. What is the
rider’s displacement during this time?
20. A sports car starting at rest can move 100.0 m in the first
4.5 s of uniform acceleration. Find the car’s acceleration.
21. A toy car is given an initial velocity of 5.0 m/s and
experiences a constant acceleration of 2.0 m/s2. What is
the final velocity after 6.0 s?
22. A shopping cart given an initial velocity of 2.0 m/s
undergoes a constant acceleration of 3.0 m/s2. What is
the magnitude of the cart's displacement after the first
10. A motor bike accelerates from rest at a rate of 3.5 m / s 2 .
4.0 s of its motion?
How fast will it be moving by the end of 4.2 s?
11. A sports car slows to a stop with an acceleration of
-2.5 m / s 2 . How long will it take the car to stop if it was
moving at a speed of 40 m/s?
12. A car starting from rest accelerates down the street.
How far will the car have moved if it attains a speed of
20 m/s in 6.5 s?
23. A rolling ball has an initial velocity of 1.6 m/s and a
2
constant acceleration of -0.33 m/s ;
a. What is its velocity after 3.6 s?
b. How far did it travel in this time?
24. The speed limit on a particular freeway is 28.0 m/s. A car
that is merging onto the freeway is capable of
accelerating at 2.25 m/s2. If the car is currently traveling
forward at 13.0 m/s, what is the shortest amount of time
it could take the vehicle to reach the speed limit?
13. An airplane needs to build up a speed of 108 m/s in
order to take off. If the runway is 350 m long, how much
time does the plane have to build up enough speed to
25. A bike accelerates from 0.0 m/s to 4.0 m/s in 4.0 s. What
get off the ground?
distance does it travel?
26. Determine the displacement of a plane that experiences
uniform acceleration from 66 m/s to 88 m/s for 12 s.
27. How far does a plane fly in 15 s while its velocity is
changing from 145 m/s to 75 m/s at a uniform rate of
acceleration?
Free-Fall
35. Why don’t a coin and feather fall at the same rate with
air resistance?
36. Define the term Terminal Velocity?
37. An elephant and mouse are dropped from an airplane at
the same time.
a. In the absence of air resistance which would hit the
ground first?
b. If air resistance did act on both animals, which would
29. A sailboat is moving across the water at 3.0 m/s. A
hit the ground first?
gust of wind fills its sails and it accelerates at a constant
c. If air resistance did act on both animals, which would
2.0 m/s2. At the same instant, a motorboat at rest starts
have more air resistance acting on it?
2
its engines and accelerates at 4.0 m/s . After 3.0 s have
elapsed:
38. For a freely falling object, by how much does the velocity
a. Find the velocity of the sailboat.
change during each second of fall?
b. Find the velocity of the motorboat.
39. When two objects are dropped out of an airplane at the
30. A truck is stopped at a stoplight. When the light turns
same time and air resistance is not included in the
2
problem, which of the two objects would hit the ground
green, the truck accelerates at 2.5 m/s . At the same
first? Why?
instant, a car passes the truck going at a constant
15 m/s.
40. A baseball is released at rest from the top of the
a. How long will it take the truck to catch up with the
Washington Monument. It hits the ground after falling
car?
for 6.00 s. What was the height from which the ball was
b. How far away from the light do they get when the
dropped?
truck catches up to the car.
28. An interplanetary spaceship far from any star or planet
experiences uniform acceleration from 2065.0 m/s to
4512.0 m/s in 10 s. How far does it move?
31. A speeding car is traveling at constant speed of
30.0 m/s when it passes a stopped police car. The
2
police car accelerates at 7.0 m/s . How fast will it be
going when it catches up with the speeding car?
32. A tennis ball is released at the top of a 2 m ramp and
41. A coin released at rest from the top of a tower hits the
ground after falling 1.5 s. What is the speed of the coin
as it hits the ground?
42. A tourist accidentally drops a camera from a 40.0 m high
bridge. What is the camera’s speed as it hits the water?
2
rolls down with an acceleration of 1.0 m/s . The ball
reaches the end of the ramp in 2.0 s and rolls onto the
floor. If the ball experiences an average acceleration of
2
-0.5 m/s as it rolls along the floor, how far from the
end of the ramp will the ball stop?
33. A car is traveling at 20 m/s when the driver sees a child
standing on the road. The driver takes 0.8 s to react,
2
then steps on the brakes and slows at 7.0 m/s . How
far does the car go before it stops?
34. The driver of a car going 17.3 m/s suddenly sees the
lights of a barrier 30 m ahead. It takes the driver 0.75 s
to react and apply the brakes. When finally applied,
2
the brakes cause an average acceleration of -10 m/s .
Determine whether the car hits the barrier or not.
43. Human reaction time is usually about 0.20 s. If your lab
partner holds a ruler between your finger and thumb and
releases it without warning, how far can you expect the
ruler to fall before you catch it?
44. How far does a freely falling object fall in 5 seconds when
dropped off the top of a cliff?
45. Calculate the height of a cliff when a ball dropped off it
falls at a speed of 45 m/s right before hitting the ground.
46. A squirrel drops an acorn from a tree branch that is
8.00 m from the ground.
a. How long is the acorn in the air?
b. What is the acorn’s velocity when it hits the ground?
47. A ball is dropped from a 2nd story window that is
13.00 m from the ground.
a. How long is the ball in the air?
b. With what velocity does the ball hit the ground?
48. A scientist drops a ball from a height of 9.3 m.
a. How long does it take the ball the hit the floor?
b. How fast is it going right before it hits the floor?
49. You throw your keys straight down to the ground at a
speed of 5m/s.
a. How long does it take the keys to reach the ground
13.1 m below?
b. With what velocity do the keys hit the ground?
50. You throw a ball straight down to the ground off the top
of a 100 m high cliff at a speed of 25 m/s.
a. How long does it take the ball to reach the ground?
b. How fast is the ball going right before it hits the
ground?
51. A rock is thrown straight upward with an initial velocity
of 24.5 m/s where acceleration due to gravity is
9.8 m/s2. What is the rock's displacement after 1.00 s?
52. A toy rocket is shot straight up into the air with an
initial speed of 45.0 m/s.
a. How long does it take the rocket to reach its highest
position?
b. How high does the rocket rise above the ground?
53. A superhero flying at treetop level sees the Eiffel Tower
elevator begin to free fall. If the superhero is 1.00 km
away from the tower and the elevator falls from a
height of 240.0 m;
a. How long does the hero have to save the people in
the elevator?
b. What should the hero’s average velocity be?
54. A pair of spectacles is dropped from the top of a 32.0 m
high stadium. A pen is dropped 2.0 s later. How high
above the ground is the pen when the spectacles hit?
2-Dimensial Motion
55. When an object is thrown horizontally off a high cliff,
why will the horizontal speed of the object never change
while falling down?
56. Two girls decide to jump off a diving board. Kate steps
off the diving board. Anna runs straight off the diving
board so that her initial velocity is solely horizontal. They
both leave the diving board at the same time. Which one
lands in the water first?
57. An astronaut throws a baseball horizontally with the
same initial velocity: once on the Earth, and once on the
Moon. Where does the ball travel farther? Explain your
answer.
58. At the instant a horizontally pointed gun is fired, a bullet
held at the side of the gun is dropped to the ground.
Which bullet strikes the ground first, the one fired from
the gun or the one dropped?
59. Why does a bowling ball move without acceleration
when it rolls along a bowling alley?
60. In the absence of air resistance, why does the horizontal
velocity for a projectile remain constant while the
vertical velocity of the object changes?
61. How does the downward motion of a projectile thrown
perfectly horizontally off a high cliff compare with the
motion of an object free falling from the same height?
62. In the movies, vehicles attempt to jump gaps in freeway
roads that are high above the ground. If the vehicle
leaves the edge of the road perfectly horizontal, can the
vehicle make it across the gap in the road on the other
side is at the exact same height? Explain your answer.
63. In the real world air resistance does slow the motion of
projectiles as they fly through the air. Would the answer
to #58 still be same? Explain your reasoning.
64. A ball rolls off the top of a 25 m high cliff. The ball was
rolling at 2 m/s as it left the edge of the cliff.
a. How long did it take it to hit the ground below?
b. How far from the base of the cliff did it land?
65. You accidentally throw your keys perfectly horizontally
at 5 m/s off a 200 m high cliff.
a. How long does it take them to hit the ground?
b. How far from the base of the cliff did the keys land?
66. A coin rolls along the top of a 1.33 m high desk with a
constant velocity and rolls off the edge and hits the
ground 0.25 m from the edge of the desk.
a. How long did it take the coin to hit the ground?
b. What was the velocity of the coin before it rolled off
the edge of the desk?
67. A friend throws a baseball horizontally. He releases it at
a height of 2.0 m and it lands 21 m from his front foot,
which is directly below the point at which he released
the baseball.
a. How long was it in the air?
b. How fast did he throw it?
68. A toy car is rolling across a large crate at a constant
speed of 12 m/s. As the car rolls off the edge, it hits the
ground 2 m from the base of the crate.
a. How long before the car reached the ground?
b. How tall was the crate?
69. You “accidentally” throw your keys perfectly
horizontally with a speed of 18 m/s off the edge of a 50
m high cliff that goes straight down.
a. How long were the keys in the air?
b. How far from the base of the cliff did the keys land?
78. Two criminals (Lefty & Shifty) have stolen some jewels.
Lefty has the jewels when the police start to chase him
as he runs to the top of a 60 m tall building in his
attempt to escape. Meanwhile, Shifty runs to the
convenient hot-air balloon 20 m from the base of the
building and untethers it so it begins to rise at a
70. A juggler throws a ball with an initial horizontal velocity
constant speed. Lefty tosses the bag of jewels
of +1.1 m/s and an initial vertical velocity of +5.7 m/s.
horizontally with a speed of 7.3 m/s just as the balloon
What is its acceleration at the top of its flight path?
is beginning to rise straight up in the air. What must
Make sure to consider the sign when responding.
the velocity of the balloon be for Shifty to directly catch
(upward direction as positive)
the bag of jewels that Lefty tossed off the top of the
building?
71. A rock is thrown horizontally from the top of a cliff with
Angular Launching Projectiles
an initial speed of 12 m/s. If the rock hits the ground
after 2.0 s, what is the height of the cliff?
79. Consider the trajectory of the cannonball in the diagram
below.
72. A model rocket flies horizontally off the edge of the cliff
at a velocity of 50.0 m/s. If the canyon below is 100.0 m
deep, how far from the edge of the cliff does the model
rocket land?
73. A coin rolls along the top of a 1.33 m-high desk with a
constant velocity. It reaches the edge of the desk and
hits the ground 0.25 m from the edge of the desk. What
was the velocity of the coin as it rolled across the desk?
a.
b.
c.
d.
Where is the vertical velocity largest?
Where is the horizontal velocity largest?
Where is the vertical velocity smallest?
Where is the acceleration smallest?
74. A cannon is fired horizontally from atop a 40.0 m tower.
80. A projectile is launched at an angle into the air.
The cannonball travels 145 m horizontally before it
Neglecting air resistance, what is its vertical
strikes the ground. With what velocity did the ball leave
acceleration? What is its horizontal acceleration?
the muzzle?
75. A cannon is fired horizontally from atop a 30.0 m tower. 81. When kicking a soccer ball, at what angle should the ball
be kicked to make it go the highest possible distance?
The cannonball travels 122 m horizontally before it
strikes the ground. With what velocity did the ball leave
82. When kicking a soccer ball, at what angle should the ball
the muzzle?
be kicked to make it go the farthest possible distance?
76. The muzzle velocity of an armor-piercing round fired
from an M1A1 tank is 1770 m/s (4000 mph or mach
5.2). A tank is at the top of a cliff and fires a shell
horizontally. If the shell lands 6520 m from the base of
the cliff, how high is the cliff?
77. A box is dropped from a spacecraft moving horizontally
at 27.0 m/s at a distance of 155 m above the surface of
a moon. The rate of freefall acceleration on this airless
moon is 2.79 m/s2.
a. How long does it take for the box to reach the
moon's surface?
b. What is its horizontal displacement?
c. What is its vertical velocity when it strikes the
surface?
83. An archer wants to shoot an arrow from their bow and
stands 30 m from the target. If the Archer’s bow and
arrow stands at exactly the same height of the bull’s-eye
on the target, will the archer hit the bull’s-eye if they aim
perfectly horizontally? Why?
84. When shooting a gun when deer hunting, hunters use a
scope on the top of their gun to help them target the
deer better than using just their own eyeball. If the
scope is working properly, the hunter must focus the
scope before shooting. When the scope is focused it
causes it to raise or lower at an angle which causes the
hunter to raise or lower the end of their gun. How does
the raising and lowering of the end of the gun help a
hunter have a better chance of hitting the target when it
is farther away?
85. A rock is thrown straight upward with an initial velocity 90. A bullet is fired from a gun at a 37 angle with a speed
of 19.6 m/s. How much time elapses between the rock's
of 93 m/s.
being thrown and its return to the original launch
a. What are the vertical (y) and horizontal (x)
point?
components of the bullet’s velocity?
b. How long was the bullet in the air before reaching
86. A juggler throws a ball straight up into the air and it
the same height as it was fired from?
takes 1.20 seconds to reach its peak. How many
c. How high did the bullet reach before coming back
seconds will it take after that to fall back into his hand?
down?
Assume he throws and catches the ball at the same
d. How far did the bullet travel?
height.
91. A cannon is fired at an angle of 27 with the horizontal
87. You are a policeman and you arrive on the scene of an
with a velocity of 12 m/s.
accident and find that a victim was shot at an angle of
a. What are the vertical (y) and horizontal (x)
63 above the horizontal and that the bullet entered
components of the velocity of the cannon ball?
the body at a speed of 93 m/s. In order to search for
b. How long was the cannon ball in the air before it
the gun that hit the victim you need to figure out the
reached the same height from which the cannon was
following things:
originally fired?
a. What was the horizontal velocity of the bullet?
c. How high did the cannon ball reach before coming
b. What was the initial vertical velocity of the bullet?
back down?
c. How long was the bullet in the air, total?
d. How far did the cannon ball travel?
d. What was the maximum height the bullet attained?
e. What was the total horizontal distance the bullet
92. A soccer player kicks a ball into the air at an angle of
travel across town?
36 above the horizontal. The initial velocity of the ball
is 30.0 m/s.
88. To test a cannon, it is set up in a perfectly flat dessert
a. How long is the soccer ball in the air?
away from populated areas and at an inclined angle of
b. What is the horizontal distance traveled by the
55 above the horizontal. When the cannon is fired,
soccer ball?
the shell leaves the end of the cannon barrel at a
c. What is the maximum height reached by the soccer
velocity of 222 m/s.
ball?
a. What is the horizontal velocity of the shell as it flies
through the air?
93. A track star in the long jump goes into the jump at
b. What is the vertical velocity with which the shell
12 m/s and launches at 20.0° above the horizontal. How
leaves the cannon?
long is she in the air before returning to Earth?
c. When the shell is fired, for how long is the shell in
the air, total?
94. A firefighter 50.0 m away from a burning building
d. What is the maximum height the shell attains before
directs a stream of water from a fire hose at an angle of
coming down?
30 above the horizontal. If the velocity of the stream
e. What is the range of the cannon at this angle?
is 40.0 m/s, at what height will the stream of water
strike the building?
89. An arrow is shot up at an angle so that it will fly
through the air and hit a target placed at the same
95. A baseball is hit directly in line with an outfielder at an
height as the arrow was initially shot. The arrow was
angle of 35 above the horizontal with an initial
shot at a 40 angle above the horizontal with a speed
velocity of 22.0 m/s. The outfielder starts running as
of 70 m/s.
soon as the ball is hit at a constant velocity of 2.5 m/s
a. What is the horizontal velocity of the arrow as it flies
and barely catches the ball. Assuming that the ball is
through the air?
caught at the same height at which the ball was hit,
b. What is the vertical velocity with which the arrow
what was the initial separation between the hitter and
leaves the cannon?
the outfielder? (there are two possible answers)
c. When the shell is fired, for how long is the arrow in
the air, total?
d. What is the maximum height the arrow attains
before coming down?
e. What is the range of the arrow at this angle?