1
An airplane flying at 90 m/s, east is accelerated uniformly at
the rate of 0.5 m/s2, east, for ten seconds. What is its final
velocity in:
(a) m/s
(b) Km/h?
7
Answer
Answers
+8.6 m/s
15.6 meters
(a) 95 m/s, east,
(b) 342 km/h, east
2
3
A car moving at 10 m/s is uniformly accelerated at the rate of
0.50 m/s2
(a) Draw a velocity time graph of the motion
(b) What is the speed of the car 6.0 s after the acceleration
begins?
(c) How far does the car move during the 6.0 s?
8
Answer
(a) graph-linear
(b) 13 m/s
(c) 69 m
(a)
(b)
(c)
(d)
In 1991 at Smith College, in Massachusetts, Ferdie Adoboe ran
backward for a distance of 1.00 x 102 m in 13.6 s. Suppose it
takes Adoboe 2.00 s to achieve a speed equal to her average
speed during the run. Find the magnitude of her average
acceleration during the first 2.00 s.
Alternate Interpretation
9
In 1991, four English teenagers built an electric car that could
attain a speed of 30.0 m/s. Suppose it takes 8.0 s for this car to
accelerate from 18.0 m/s to 30.0 m/s
(a) What is the magnitude of the car's acceleration?
(b) What is the displacement of the car?
Answers
-1500 m/s2
10
Capt. Charles Yeager performed the first supersonic flight in
1947. He flew at a speed of 3.00 x 102 m/s at an altitude of
more than 12 km, where the speed of sound in air is slightly
less than 3.00 x 102 m/s. Suppose Capt. Yeager accelerated
from 1.20 x 102 m/s to 3.00 x 102 m/s in 25.0 s. What was the
magnitude of his acceleration?
6
A car traveling in a straight line has a velocity of +5.0 m/s.
After 4.0 s; its velocity is +8.0 m/s.
(a) What is the car's average acceleration in this time interval?
(b) What is the car’s displacement?
Answer
(a) +.75 m/s2
(b) 26 m
As a shuttle bus comes to a normal stop, it slows from 9.00 m/s
to 0.00 m/s in 5.00 s. (Draw a Velocity -Time Graph and list
the information)
(a) Find the average acceleation of the bus.
(b) Find the displacement of the bus.
Answer
(a) -1.80 m/s2
(b) 22.5 m
11
7.20 m/s2
A tennis ball with a velocity of +10.0 m/s to the right is thrown
perpendicularly at a wall. After striking the wall, the ball
rebounds in the opposite direction with a velocity of -8.0 m/s to
the left. If the ball is in contact with the wall for 0.012 s, what
is the average acceleration of the ball while it is in contact with
the wall? (Make sure you draw a picture and sketch a graph
Answer
(a) 1.5 m/s2
(b) 192 m
Answers
+6.5 m/s
33.25 m
5.0 s
7.2 meters
(c) 10.8 s
(d) 35.2 m
-3.68 m/s2
5
A snowmobile has an initial velocity of +3.0 m/s.
(a) If it accelerates at the rate of +0.50 m/s2 for 7.0 s, what is
the final velocity?
(b) What is its displacement during that time interval?
(c) If it accelerates at the rate of -0.60 m/s2 , how long will it
take to come to a complete stop?
(d) What is its displacement during that time interval?
Answers
Answers
Hard
4
A car traveling at +7.0 m/s accelerates at the rate of +0.80 m/s2
for an interval of 2.0 s.
(a) Find vf
(b) Find the displacement.
When A shuttle bus comes to a sudden stop to avoid hitting a
dog, it slows from 9.00 m/s to 0.00 m/s in 1.50 s. (Draw a
Velocity -Time Graph and list the information)
(a) Find the average acceleation of the bus.
(b) Find the displacement of the bus.
Answer
(a) -6.00 m/s2
(b) 6.75 m
12
13
A car traveling initially at 7.0 m/s accelrates to a velocity of
12.0 m/s in 2.0 s. (Draw a Velocity -Time Graph and list the
information)
(a) Find the average acceleation of the bus.
(b) Find the displacement of the bus.
18
A sports car with an average accleration of 5.1 m/s2 reaches a
velocity of 27 m/s from rest. (Draw a Velocity -Time Graph
and list the information)
(a) How long does it take?
(b) How far does it travel when it reaches that velocity?
Answer
Answer
(a) 2.5 m/s2
(b) 19 m
(a) 5.3 seconds
(b) 71.415 m
Turner’s treadmill starts with a velocity of -1.2 m/s and speeds
up at regular intervals during a half hour workout. After 25
minutes, the treadmill has a velocity of -6.5 m/s. (Draw a
Velocity -Time Graph and list the information)
(a) What is the average acceleration of the tredmill during this
period?
(b) What is the displacement of the treadmill durng this period
19
A bicyclist accelerates from 5.0 m/s to a velocity of 16 /s in 8
s. (Draw a Velocity -Time Graph and list the information)
(a) Assuming constant acceleration, what distance does the
bicyclist travel during this interval?
(b) What is his acceleration during this time interval?
Answer
Answer
(a) 84 m
(b) 1.38 m/s2
(a) -3.5 x10-3m/s2
(b) -5775 m
20
14
If a treadmill starts at a veloocity of -2.7 m/s and has a velocity
of -1.3 m/s after 5.0 min. (Draw a Velocity -Time Graph and
list the information)
(a) What is the average acceleation of the treadmill?
(b) Find the displacement of the treadmill
While a baseball is being hit, its speed changes from -35 m/s to
+52 m/s in a time interval of 0.10 s. (Draw a Velocity -Time
Graph and list the information
(a) Assuming constant acceleration, what is the ball’s
displacement during this time interval?
(b) What is the path length of the baseball during this time
interval
(c) What is the acceleration of the baseball?
Answer
Answer
(a) 4.7 x 10-3 m/s2
(b) -600 m
15
A cyclist has an initial velocity of 13.5 m/s and an acceleraiton
of -0.50 m/s2. (Draw a Velocity -Time Graph and list the
information)
(a) How long will it take a cyclist to bring a bicycle to a
complete stop?
(b) How far did the bicyclist travel when he came to a
complete stop?
(a) .85 m
(b)
(c)
21
Answer
(a) 27 s
(b) 182.25 m
John Howard of the United States reached the highest speed
ever achieved on a bicycle. The bicycle, which was accelerated
by being towed by a vehicle, reached a speed of 245 km/h.
Suppose Howard wants to slow down and applies the brakes on
his now freely moving bicycle. If the average deceleration of
the bicycle has a magnitude of 3.00 m/s2, how long will it take
for the bicycle's speed to decrease by 20.0 percent?
Answer
4.57 s
16
An amusement park ride that falls from rest to a speed of 28
m/s in 3.0 s. (Draw a Velocity -Time Graph and list the
information)
(a) Find the acceleration of the amusement park ride.
(b) How far does it travel in the 3.0 seconds?
22
A boy sledding down a hill accelerates at 1.40 m/s2. If he
started from rest, in what distance would he reach a speed of
7.00 m/s?
Answer
Answer
17.5 m
(a) 9.3 m/s2
(b)
23
17
A motorcycle with an average accleration of 15 m/s2 reaches a
velocity of 27 m/s from rest. (Draw a Velocity -Time Graph
and list the information)
(a) How long does it take?
(b) How far does it travel when it reaches that velocity?
Answer
(a) 1.8 seconds
(b)
The polar bear is an excellent swimmer, and it spends a large
part of its time in the water. Suppose a polar bear wants to
swim from an ice floe to a particular point on shore where it
knows that seals gather. The bear dives into the water and
begins swimming with a speed of 2.60 m/s. By the time it
arrives at the shore, its speed has decreased to 2.20 m/s. If the
polar bear's swim takes exactly 9.00 min and it has a constant
deceleration, what is the distance traveled by the polar bear?
Answer
1.2906 m
24
A racing car reaches a speed of 42 m/s. It then begins a
uniform negative acceleration, using its parachute and braking
system, and comes to rest 5.5 s later. (Draw a Velocity -Time
Graph and list the information)
(a) Find how far the car moves while stopping?
(b) What is the acceleration of the car?
29
A car enters the freeway with a speed of 23 km/h and
accelerates to a speed of 86 km/h in 3.5 min. (Draw a Velocity
-Time Graph and list the information)
(a) How far does the car move while accelerating?
(b) What is the acceleration? Give your answer in m/s
Answer
Answer
(a) 3168 m
(b) .083 m/s2
1080 km/hr2
(a) 115 m
(b) -7.64 m/s2
25
26
A car accelerates uniformly from rest to a speed of 23.7 km/h
in 6.5 s. (Draw a Velocity -Time Graph and list the
information)
(a) Find the distance the car travels during this time.
(b) What is the acceleration of the car?
30
Answer
Answer
(a) 21 m
(b) 1.01 m/s2
(a) +1.6 m/s2
(b) +24 m/s
(c) 240m
When Maggie applies the brakes of her car, the car slows
uniformly from 15.00 m/s to 0.00 m/s in 2.50 s. (Draw a
Velocity -Time Graph and list the information)
(a) How many meters before a stop sign must she apply her
brakes in order to stop at the sign?
(b) What is her acceleration?
31
(a) 18.8 m
(b) -6m/s2
A car accelerates uniformly from rest to a speed of 65 km/h (18
m/s) in 12 s. Find the distance the car travels during this time.
Answer
110 m
Answer
27
A car moving westward along a straight, level road increases
its velocity uniformly from +16 m/s to +32 m/s in 10.0 s.
(a) What is the car's acceleration?
(b) What is its average velocity?
(c) How far did it move while accelerating?
32
A jet plane lands with a velocity of +100 m/s and can
accelerate at a maximum rate of -5.0 m/s2 as it comes to rest.
Can this plane land at an airport where the runway is 0.80 km
long? (Draw a Velocity -Time Graph and list the information)
A dump truck with an average accleration of 0.80 m/s2 reaches
a velocity of 27 m/s from rest. (Draw a Velocity -Time Graph
and list the information)
(a) How long does it take?
(b) How far does it travel when it reaches that velocity?
Answer
(a) 34 seconds
(b) 455 m
Answer
No; the plane needs 1 km to land.
note
.058 hr
.1086 km/hr
28
33
A driver in a car traveling at a speed of 78 km/h sees a cat 100m away on the road. (Draw a Velocity -Time Graph and list the
information)
(a) How long will it take for the car to accelerate constantly to
a stop in exactly 99-m?
(b) What is the acceleration on the driver? Give your answer
in m/s.
Answer
(a) 9.1 s
.00253 h
(b) -2.38 m/s2
3, 0844 km/hr2
A pedestrian is running at his maximum speed of 6 m/s to
catch a bus stopped by a traffic light. When he is 10 meters
from the bus, the light changes and the bus accelerates
uniformly at 1.0 m/s2. Find how far he has to run to catch the
bus or his FRUSTRATION DISTANCE (closest approach)
HINT: Do the problem by the use of a distance time graph and
by applying the appropriate kinematic equations.
Answer
Hard
34
A plane starting at rest at one end of a runway undergoes a
constant acceleration of 4.8 m/s2 for 15 s before takeoff.
(a) What is its speed at take off?
(b) How long must the runway be for the plane to be able to
take off?
Answer
(a) 72 m/s
(b) 540 m
35
A car with an initial speed of 23.7 km/h accelerates at a
uniform rate of 0.92 m/s2 for 3.6 s. Find the final speed and the
displacement of the car during this time.
42
Answer
(a) 36 km/hr
9.9 m/s
(b) +0.030 km
+29.6 m
36
An automobile with an initial speed of 4.30 m/s accelerates at
the rate of 3.00 m/s2. Find the final speed and the displacement
after 5.0 s.
Answer
(a) 2.18 m/s
(b) 4.36 seconds
43
Answer
(a) 19 m/s
(b) 59 m
37
38
A car starts from rest and travels for 5.0 s with a uniform
acceleration of -1.5 m/s2.
(a) What is the final velocity of the car?
(b) How far does the car travel in this time interval?
A baby sitter pushing a stroller starts from rest and accelerates
at a rate of 0.500 m/s2.
(a) What is the velocity of the stroller after it has traveled 4.75
m?
(b) How long does it take to reach that velocity?
An aircraft has a landing speed of 302 km/h. The landing area
of an aircraft carrier is 195 m long.
(a) What is the minimum constant acceleration required for a
safe landing?
(b) How long does it take to come to a stop once it has landed?
Answer
Board Problem
(a) -18.0 m/s2
(b) 4.65 seconds
Answer
An electron is accelerated from rest in an accelerator at 4.5 x
107 m/s2 over a distance of 95 km.
(a) Assuming constant acceleration, what is the final velocity
of the electron?
(b) What is the time it takes to reach it’s final velocity?
(a) -7.5 m/s
(b) 18.8 m
Answer
A driver of a car traveling at - 15 m/s applies the brakes,
causing a uniform acceleration of +2.0 m/s2. The brakes are
applied for 2.5 s.
(a) What is the velocity of the car at the end of the braking
period?
(b) How far has the car moved during the braking period?
44
(a) 2.92 x 106 m/s
(b) .065 seconds
45
A baby sitter pushing a stroller starts from rest and accelerates
at a rate of 0.500 m/s2.
(a) What is the velocity of the stroller after the stroller has
traveled 6.32 m.
(b) What is the time it takes to reach the final velocity?
Answer
Answer
(a) -10 m/s
(b) -31.3 m
39
A ball initially at rest rolls down a hill with an acceleration of
3.3 m/s2. If it accelerates for 7.5 s, how far will it move?
(a) +2.51 m/s
(b) 5 seconds
46
Answer
92.8 m
A car traveling initially at +7.0 m/s accelerates at the rate of
+0.80 m/s2 for a distance of 245 m.
(a) What is its velocity and time at the end of the acceleration?
(b) What is its velocity and time after it accelerates for 125 m?
(c) What is its velocity and after it accelerates for 67 m?
Answer
40
A car accelerates from rest at -3.00 m/s2
(a) What is the velocity at the end of 5.0 s?
(b) What is the displacement after 5.0 s?
(a) -21 m/s
17.5 seconds
(b) +15.8 m/s
11.25 seconds
(c) 12.5 m/s
6,8 seconds
Answer
(a) 15 m/s
(b) -38 m
41
A box falls off the tailgate of a truck and slides along the street
for a distance of 62.5 m. Friction decelerates the box at 5.0
m/s2 until it stops. At what speed was the truck moving when
the box fell?
Answer
25 m/s
47
A gull soaring in a straight line with an initial velocity of -32
m/s accelerates at a rate of +3.0 m/s2 for 9.0 s.
(a) What is the gull's velocity at the end of the acceleration?
(b) What is the displacement of the gull at the end of the 9.0 s?
Answer
(a) -5 m/s
(b) -166.5 m
48
An aircraft has a lift off speed of 120 km/h.
(a) What minimum constant acceleration does this require if
the aircraft is to be airborne after a take-off run of 240 m? Give
your answer in m/s2.
(b) How long does it take the aircraft to become airborne?
54
A speedboat increases its velocity from 25 m/s to the west to
35 m/s to the west in a distance of 250 m.
(a) Find the magnitude of the boat's acceleration.
(b) Find the time it takes the boat to travel this distance.
Answer
(a) 1 m/s2
to the west
(b) 8.3 s
Answer
(a) 2.3 m/s2
30,000 km/hr2
(b) 14.4 s
55
49
A car accelerates in a straight line from rest at the rate of 2.3
m/s2.
(a) What is the speed of the car after it has traveled 55 m?
(b) How long does it take the car to travel 55 m?
A plane lands with a velocity of +120 m/s and accelerates at a
maximum rate of -6.0 m/s2
(a) From the instant the plane touches the runway, what is the
minimum time needed before it can come to rest?
(b) Can this plane land on a naval aircraft carrier where the
runway is 0.80 km long?
Answer
Answer
(a) 15.9 m/s
(b) 6.9 s
50
Marisa’s car accelerates at a rate of +2.60 m/s2.
(a) How long does it take for Marisa’s car to accelerate from a
speed of 88.5 km/h to a speed of 96.5 km/h?
(b) What is the displacement of Marisa’s car?
(a) 2.0 x 101 s
(b) No the plane needs at least 1.2 km to land.
56
Answer
(a) 0.85 s
(b) 22,4 n
51
A plane starting at rest at the south end of a runway undergoes
a constant acceleration of +1.6 m/s2 for a distance of 1600 m
before takeoff.
(a) What is the plane's velocity at takeoff
(b) What is the time required for takeoff?
Answer
(a) 71.6 m/s
(b) 44.7 s
52
Answer
8.38 m
57
Nathan accelerates his skateboard along a stright path from rest
to 12.5 m/s in 2.5 s
(a) What is Nathan’s acceleration?
(b) What is Nathan’s displacement during this time interval?
(c) What is Nathan’s average velocity during this time
interval?
A bus slows down uniformly from 75.0 km/h (21 m/s) to 0.0
km/h in 220 m. How long does it take to stop?
Answer
Answer
(a) 5.0 m/s2
(b) 15.6 m
(c) 6.25 m/s
21 s
53
A man named Bungkas climbed a palm tree in 1970 and built
himself a nest there. In 1994 he was still up there, and he had
not left the tree for 24 years. Suppose Bungkas asks a villager
for a newspaper, which is thrown to him straight up with an
initial speed of 12.0 m/s. When Bungkas catches the
newspaper from his nest, the newspaper's velocity is 3.0 m/s,
directed upward. From this information, find the height at
which the nest was built. Assume that the newspaper is thrown
from a height of 1.50 m above the ground.
A car starts from rest and travels for 5.0 s with a uniform
acceleration of +1.5 m/s2. The driver then applies the brakes,
causing a uniform acceleration of -2.0 m/s2. If the brakes are
applied for 3.0 s, how fast is the car going at the end of the
braking period, and how far has it gone from its start?
Answer
+1.5 m/s
32.3 m
58
You are driving toward a traffic signal when it turns yellow.
Your speed is the legal speed limit of v0 = 55 km/h; your best
deceleration rate has the magnitude a = 5.18 m/s2. Your best
reaction time to begin braking is T = 0.75 s.
(a) To avoid having the front of your car enter the intersection
after the light turns red, should you brake to a stop or continue
to move at 55 km/h if the distance to the intersection and the
duration of the yellow light is 40 m and 2.8 s?
(b) To avoid having the front of your car enter the intersection
after the light turns red, should you brake to a stop or continue
to move at 55 km/h if the distance to the intersection and the
duration of the yellow light is 32 m and 1.8 s? Give an answer
of brake, continue, either (if either strategy works), or neither
(if neither strategy works).
62
A basketball player grabbing a rebound jumps 76.0 cm
vertically.
(a) How much total time (ascent and descent) does the player
spend in the top 15.0 cm of this jump
(b) How much total time (ascent and descent) does the player
spend in the bottom 15.0 cm?
(c) Do your results explain why such players seem to hang in
the air at the top of a jump?
Answer
(a) 350 ms;
(b) 82 ms (each includes both ascent and descent through
the 15 cm)
Answer
Hard
(a) either;
(b) neither
59
63
A shuffleboard disk is accelerated at a constant rate from rest
to a speed of 6.0 m/s over a 1.8 m distance by a player using a
cue. At this point the disk loses contact with the cue and slows
at a constant rate of 2.5 m/s2 until it stops.
(a) How much time elapses from when the disk begins to
accelerate until it stops?
(b) What total distance does the disk travel?
Answer
Hard Problem
Answer
(a) 60.6 s;
(b) 36.3 m/s
64
(a) 3.0 s;
(b) 9.0 m
60
A test rocket is fired vertically upward from a well. A catapult
gives it initial velocity 80.0 m/s at ground level. Its engines
then fire and it accelerates upward at 4.00 m/s2 until it reaches
an altitude of 1,000 m. At that point its engines fail and the
rocket goes into free fall, with an acceleration of –9.80 m/s2.
(a) How long is the rocket in motion above the ground?
(b) What is its maximum altitude?
(c) What is its velocity just before it collides with the Earth?
The maximum acceleration that is tolerable for passengers in a
subway train is 1.34 m/s2 and subway stations are located 806
m apart.
(a) What is the maximum speed a subway train can attain
between stations?
(b) What is the travel time between stations?
(c) If a subway train stops for 20 s at each station, what is the
maximum average speed of the train, from one start-up to the
next?
(d) Graph x, v, and a versus t for the interval from one start-up
to the next.
Answer
(a) 32.9 m/s;
(b) 49.1 s;
(c) 11.7 m/s
An ice sled powered by a rocket engine starts from rest on a
large frozen lake and accelerates at +13.0 m/s2. At t1 the rocket
engine is shut down and the sled moves with constant velocity
v until t2. The total distance traveled by the sled is 5.30 x 103 m
and the total time is 90.0 s. Find t1, t2, and v.
Answer
Hard
4.6 s
85.3 s
+61 m/s
65
Answer
61
Two subway stops are separated by 1100 m. A subway train
accelerates at +1.2 m/s2 from rest through the first half of the
distance and decelerates at -1.2 m/s2 through the second half.
(a) What is its travel time?
(b) What is its maximum speed?
(c) Graph x, v, and a versus t for the trip.
A ranger in a national park is driving at 56 km/h when a deer
jumps onto the road 65 m ahead of the vehicle. After a reaction
time of t seconds, the ranger applies the brakes to produce an
acceleration of -3.0 m/s2. What is the maximum reaction time
allowed if the ranger is to avoid hitting the deer?
Answer
Hard
1.57 s
66
A speeder passes a parked police car at 30.0 m/s. The police
car starts from rest with a uniform acceleration of 2.44 m/s2
(a) How much time passes before the police car overtakes the
speeder?
(b) How far does the police car get before overtaking the
speeder?
(c) What is the speed of the police car when he catches the
speeder?
Answer
Hard
(a) 24.6 s
(b) 738 m
(c) 60.02 m/s
67
A mountain climber stands at the top of a 50.0-m cliff hanging
over a calm pool of water. The climber throws two stones
vertically 1.0 s apart and observes that they cause a single
splash when they hit the water. The first stone has an initial
velocity of +2.0 m/s.
(a) How long after release of the first stone will the two stones
hit the water?
(b) What is the initial velocity of the second stone when it is
thrown?
(c) What will the velocity of each stone be at the instant both
stones hit the water?
70
Answer
Hard
Answer
Hard
(a) 3.40 s
(b) -9.2 m/s
(c) -31.4 m/s;
33 m/s
68
A professional race car driver buys a car that can accelerate at
+5.9 m/s2. The racer decides to race against another driver in a
souped-up stock car. Both start from rest, but the stock-car
driver leaves 1.0 s before the driver of the sports car. The stock
car moves with a constant acceleration of +3.6 m/s2
(a) Find the time it takes the sports-car driver to overtake the
stock-car driver.
(b) Find the distance the two drivers travel before they are side
by side.
(c) Find the velocities of both cars at the instant they are side
by side.
An ice sled powered by a rocket engine starts from rest on a
large frozen lake and accelerates at +13.0 m/s2. At t1 the rocket
engine is shut down and the sled moves with constant velocity
v until t2. The total distance traveled by the sled from start to t2
is 5300 m and the total time is 90.0 s. At the 5800 in mark, the
sled begins to accelerate at -7.0 m/s2.
(a) Find t1
(b) Find t2
(c) Find v
(d) What is the final position of the sled from the start when it
comes to rest?
(e) How long does it take for the sled to come to rest
from the 5800 mark?
(a)
(b)
(c)
(d)
(e)
71
Answer
4.6 s
85 s
60 m/s
6083 m
8.64 s
In the figure, a red car and a green car, identical except for the
color, move toward each other in adjacent lanes and parallel to
an x axis. At time t = 0, the red car is at x0 = 0 and the green
car is at x0 = 220 m. If the red car has a constant velocity of 20
km/h, the cars pass each other at x = 44.5 m, and if it has a
constant velocity of 40 km/h, they pass each other at x = 76.6
m.
(a) What is the initial velocity of the green car?
(b) What is the acceleration of the green car?
(a) 4.6 s after stock car starts
(b) 38 m’
(c) +17 m/s (stock car)
+21 m/s (sports car)
69
Two cars are traveling along a straight line in the same
direction, the lead car at 25 m/s and the other car at 35 m/s. At
the moment the cars are 45 m apart, the lead driver applies the
brakes, causing the car to have an acceleration of -2.0 m/s2.
(a) How long does it take for the lead car to stop?
(b) Assume that the driver of the chasing car applies the
brakes at the same time as the driver of the lead car. What must
the chasing car's minimum negative acceleration be to avoid
hitting the lead car?
(c) How long does it take the chasing car to stop?
Answer
Hard
(a) -50 km/h;
(b) -2.0 m/s2
72
Answer
(a) 12.5 s
(b) -3.1 m/s2
(c) 11 s
A red train traveling at 72 km/h and a green train traveling at
144 km/h are headed toward each other along a straight, level
track. When they are 950 m apart, each engineer sees the
other's train and applies the brakes. The brakes slow each train
at the rate of 1.0 m/s2. Is there a collision? If so, answer yes
and give the speed of the red train and the speed of the green
train at impact, respectively. If not, answer no and give the
separation between the trains when they stop.
Answer
Hard
yes, 0, 10 m/s
73
A robot probe drops a camera off the rim of a 24-km-deep
crater on Mars, where the free-fall acceleration is -3.7 m/s2.
(a) Find the time required for the camera to reach the crater
floor.
(b) Find the velocity with which it hits.
Answer
(a) 114 s
(b) -421 m/s
74
A pebble is dropped down a well and hits the water 1.5 s later.
Using the equations for motion with constant acceleration,
determine the distance from the edge of the well to the water's
surface.
80
A tennis ball is thrown vertically upward with an initial
velocity of +8.0 m/s.
(a) What will its speed be when it returns to its starting point?
(b) How long will it take for it to reach its starting point?
(c) How high does the tennis ball go?
Answer
Answer
11 m
75
A worker drops a wrench from the top of a tower 80.0-m tall.
With what velocity does the wrench strike the ground?
-39.6 m/s
Maria throws an apple vertically upward from a height of 1.3
m with an initial velocity of +12.4 m/s.
(a) Will the apple reach Maria's friend in a tree house 5.3 m
above the ground?
(b) If the apple is not caught, how long will the apple be in the
air before it hits the ground?
A gumdrop is released from rest at the top of the Empire State
Building, which is 381 m tall. Disregarding air resistance,
calculate the displacement and velocity of the gumdrop after
1.00, 2.00, and 3.00 s.
Answer
Answer
76
(a) 8.0 m/s
(b) 1.63 s
(c) 3.27 m
81
(a) Yes
(b) 2.63 seconds
Answer
1 Second
-4.90 m
-9.81 m/s
82
2 Seconds
-19.6 m
-19.6 m/s
Answer
3 Seconds
-44.1 m
-29.4 m/s
77
Jason hits volleyball so that it moves with an initial velocity of
6.0 m/s straight upward. If the volleyball starts from 2.0 m
above the floor, how long will it be in the air before it strikes
the floor? Assume that Jason is the last player to touch the ball
before it hits the floor?
A coin is tossed upwar(d)
(a) What happens to its velocity while it is in the air?
(b) Does its acceleration increase, decrease, or remain constant
while it is in the air?
(a) The coin’s velocity decreases becomes zero at its
maximum height. And then increases in the negative
direction until it hits the ground.
(b) the coin’s acceleration remains constant
83
A ball is thrown vertically upward. What are its velocity and
acceleration when it reaches its maximum altitude? What is its
acceleration just before it hits the ground?
Answer
Answer
Hard
At maximum altitude, v = 0 and a = -9.81 m/s2. Just before
the ball hits the ground, a = -9.81 m/s2.
1.50 s
78
Jason hits volleyball so that it moves with an initial velocity of
6.0 m/s straight upward. The volleyball starts from 2.0 m
above the floor.
(a) Calculate the displacement of the volleyball 0.50 s after
Jason hits it.
(b) Calculate the velocity of the volleyball 0.50 s after Jason
hits it.
84
A ball is thrown vertically upward.
(a) What happens to the ball's velocity while the ball is in the
air?
(b) What is its velocity when it reaches its maximum altitude?
(c) What is its acceleration when it reaches its maximum
altitude?
(d) What is its acceleration just before it hits the ground?
(e) Does its acceleration increase, decrease, or remain
constant?
Answer
(a) 1.8 m
(b) 1.1 m/s
79
Stephanie serves the volleyball from a height of 0.80 m and
gives it an initial velocity of +7.6 m/s straight up.
(a) How high will it go?
(b) How long will it take the ball to reach its maximum
height? (Hint: At maximum height, v = 0 m/s.)
Answer
(a) 3.7 m
(b) 0.77 s
Answer
(a) The ball’s velocity decreases, becomes zero at its
maximum altitude, then increases in the negative direction.
(b) At maximum altitude, the ball’s velocity is zero.
(c) -9.81 m/s2
(d) -9.81 m/s2
(e) the ball’s acceleration remains constant
85
86
A physics student throws softball straight up into the air. The
ball was in the air for a total of 3.56 s before it was caught at
its original position.
(a) What was the initial velocity of the ball?
(b) How high did it rise?
91
Answer
Answer
Hard
(a) 17.5 m/s
(b) 15.5 m
940.8 m
A ball is thrown upward from the ground with an initial speed
of 25 m/s; at the same instant, a ball is dropped from rest from
a building 15 m high. After how long will the balls be at the
same height?
92
Answer
Hard
0.60 s
87
A rocket moves upward, starting from rest with an acceleration
of +29.4 m/s2 for 4.00 s. It runs out of fuel at the end of the
4.00 s but does not stop. How high does it rise above the
ground?
Two students are on a balcony 19.6-m above the street. One
student throws a ball vertically downward at 14.7 m/s. At the
same instant; the other student throws a ball vertically upward
at the same speed. The second ball just misses the balcony on
the way down.
(a) What is the difference in the time the balls spend in the air?
(b) What is the velocity of each ball as it strikes the ground?
(c) How far apart are the balls 0.800 s after they are thrown?
Answer
(a) 3.0 s
(b) -24.5 m/s
-24.5 m/s
(c) 23.6 m
A peregrine falcon dives at a pigeon. The falcon starts
downward from rest with free-fall acceleration. If the pigeon is
76.0 m below the initial position of the falcon, how long does it
take the falcon to reach the pigeon? Assume that the pigeon
remains at rest.
93
Answer
3.94 s
A small fish is dropped by a pelican that is rising steadily at
0.50 m/s.
(a) After 2.5 s, what is the velocity of the fish?
(b) How far below the pelican is the fish after 2.5 s?
Answer
88
A juggler throws a bowling pin into the air with an initial
velocity vi. Another juggler drops a pin at the same instant.
Compare the accelerations of the two pins while they are in the
air.
Answer
(a) -24 m/s
(b) 31 m
94
The two pins have the same acceleration (-9.81 m/s2)
89
A flowerpot falls from a windowsill 25.0 m above the
sidewalk.
(a) How fast is the flowerpot moving when it strikes the
ground?
(b) How much time does a passerby on the sidewalk below
have to move out of the way before the flowerpot hits the
ground?
Answer
(a) -22.1 m/s
(b) 2.25 s
90
Two children are bouncing small rubber balls. One child
simply drops a ball. At the same time, the second child throws
a ball downward so that it has an initial speed of 10 m/s. What
is the acceleration of each ball while in motion?
Answer
-9.81 m/s2
A parachutist descending at a speed of 10.0 m/s loses a shoe at
an altitude of 50.0 m.
(a) When does the shoe reach the ground?
(b) What is the velocity of the shoe just before it hits the
ground?
(c) How high is the parachutist when the show hits the floor
Answer
(a) 2.33 s
(b) -32.88 m/s
(c) 26.7 m
95
A small first-aid kit is dropped by a rock climber who is
descending steadily at 1.9 m/s.
(a) What is the velocity of the first-aid kit after 2.5 s?
(b) How far is the kit below the climber after 2.5 s?
Answer
-26.4 m/s
30.8 m
96
A model rocket is launched straight upward with an initial
speed of 50.0 m/s. It accelerates with a constant upward
acceleration of 2.00 m/s2 until its engines stop at an altitude of
150 m.
(a) What is the maximum height reached by the rocket?
(b) When does the rocket reach maximum height?
(c) How long is the rocket in the air?
100
Water drips from the nozzle of a shower onto the floor 200 cm
below. The drops fall at regular (equal) intervals of time, the
first drop striking the floor at the instant the fourth drop begins
to fall.
(a) When the first drop strikes the floor, how far below the
nozzle is the second drop?
(b) When the first drop strikes the floor, how far below the
nozzle is the third drop?
Answer
Hard
Answer
Hard
(a) 308 m
(b) 8.53 s
(c) 16.4 s
97
A hot-air balloon is ascending at the rate of 12 m/s and is 80 m
above the ground when a package is dropped over the side.
(a) How long does the package take to reach the ground?
(b) With what speed does it hit the ground?
(a) 89 cm;
(b) 22 cm
101
Answer
Hard
(a) 5.4 s;
(b) 41 m/s
98
Answer
Hard
A bolt is dropped from a bridge under construction, falling 90
m to the valley below the bridge.
(a) In how much time does it pass through the last 20% of its
fall?
(b) What is its speed when it begins that last 20% of its fall?
(c) What is its speed when it reaches the valley beneath the
bridge?
(a) 350 ms;
(b) 82 ms (each includes both ascent and descent through
the 15 cm)
102
Answer
Hard
(a) 0.45 s;
(b) 38 m/s;
(c) 42 m/s
99
20.4 m
103
(a) 12.3 m/s
(b)
A steel ball is dropped from a building's roof and passes a
window, taking 0.125 s to fall from the top to the bottom of the
window, a distance of 1.20 m. It then falls to a sidewalk and
bounces back past the window, moving from bottom to top in
0.125 s. Assume that the upward flight is an exact reverse of
the fall. The time the ball spends below the bottom of the
window is 2.00 s. How tall is the building?
Answer
Hard
A stone is dropped into a river from a bridge 43.9 m above the
water. Another stone is thrown vertically down 1.00 s after the
first is dropped. The stones strike the water at the same time.
(a) What is the initial speed of the second stone?
(b) Plot velocity versus time on a graph for each stone, taking
zero time as the instant the first stone is released.
Answer
Hard
A basketball player grabbing a rebound jumps 76.0 cm
vertically.
(a) How much total time (ascent and descent) does the player
spend in the top 15.0 cm of this jump
(b) How much total time (ascent and descent) does the player
spend in the bottom 15.0 cm?
(c) Do your results explain why such players seem to hang in
the air at the top of a jump?
A lead ball is dropped in a lake from a diving board 5.20 m
above the water. It hits the water with a certain velocity and
then sinks to the bottom with this same constant velocity. It
reaches the bottom 4.80 s after it is dropped.
(a) How deep is the lake?
(b) What is the magnitude of the average velocity of the ball
for the entire fall?
(c) What is the direction (up or down) of the average velocity
of the ball for the entire fall? Suppose that all the water is
drained from the lake. The ball is now thrown from the diving
board so that it again reaches the bottom in 4.80 s.
(d) What is the magnitude of the initial velocity of the ball?
(e) What is the direction of the initial velocity of the ball?
Answer
(a) 38.1m;
(b) 9.02 m/s;
(c) down;
(d) 14.5 m/s;
(e) up
104
Two diamonds begin a free fall from rest from the same height,
1.0 s apart. How long after the first diamond begins to fall will
the two diamonds be 10 m apart?
Answer
1.5 s
105
A lead ball is dropped in a lake from a diving board 5.20 m
above the water. It hits the water with a certain velocity and
then sinks to the bottom with this same constant velocity. It
reaches the bottom 4.80 s after it is dropped.
(a) How deep is the lake?
(b) What is the magnitude of the average velocity of the ball
for the entire fall?
(c) What is the direction (up or down) of the average velocity
of the ball for the entire fall? Suppose that all the water is
drained from the lake. The ball is now thrown from the diving
board so that it again reaches the bottom in 4.80 s.
(d) What is the magnitude of the initial velocity of the ball?
(e) What is the direction of the initial velocity of the ball?
Answer
My Solution
(a) 38.1m;
(b) 9.02 m/s;
(c) down;
(d) 14.5 m/s;
(e) up