PHYS-1401: College Physics-I
CRN 55178
HOMEWORK PROBLEMS
Khalid Bukhari
HW-2
Chapter 2: MOTION IN ONE DIMENSION
PART-A: Hand in your answers in class on scantron on Wednesday 19 September-2010
1. An arrow is shot straight up in the air at an initial speed of 15.0 m/s. After how much time is the
arrow heading downward at a speed of 8.00 m/s? (a) 0.714 s (b) 1.24 s (c) 1.87 s (d) 2.35 s (e) 3.22 s
t 
v f  v0
8.00 m s   15.0 m s 
v


 2.35 s
a
g
 9.80 m s2
2. A cannon shell is fired straight up in the air at an initial speed of 225 m/s. After how much time is the
shell at a height of 6.20 X 102 m and heading down? (a) 2.96 s (b) 17.3 s (c) 25.4 s (d) 33.6 s (e) 43.0 s
y  v 0 t 
1
2
gt 2
6.20  102 m   225 m s  t 
 4.90
t 
1
9.80 m s2 t 2
2



m s2 t 2   225 m s  t  6.20  10 2 m  0
  225 m s  
 225

m s   4 4.90 m s 2
2

2 4.90 m s2

  6.20  10 2 m 
with solutions of t = 43.0 s and . t = 2.94 s The projectile is at a height of 6.20  102 m and coming downward at the largest
of these two elapsed times, so the correct choice is seen to be (e).
3. When applying the equations of kinematics for an object moving in one dimension, which of the
following statements must be true? (a) The velocity of the object must remain constant. (b) The
acceleration of the object must remain constant. (c) The velocity of the object must increase with time.
(d) The position of the object must increase with time. (e) The velocity of the object must always be in
the same direction as its acceleration.
4. A juggler throws a bowling pin straight up in the air. After the pin leaves his hand and while it is in
the air, which statement is true? (a) The velocity of the pin is always in the same direction as its
acceleration. (b) The velocity of the pin is never in the same direction as its acceleration. (c) The
acceleration of the pin is zero. (d) The velocity of the pin is opposite its acceleration on the way up. (e)
The velocity of the pin is in the same direction as its acceleration on the way up.
5. A racing car starts from rest and reaches a final speed v in a time t. If the acceleration of the car is
constant during this time, which of the following statements must be true? (a) The car travels a distance
vt. (b) The average speed of the car is v/2. (c) The acceleration of the car is v/t. (d) The velocity of the
car remains constant. (e) None of these
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PHYS-1401: College Physics-I
CRN 55178
Khalid Bukhari
HW-2
6. A pebble is dropped from rest from the top of a tall cliff and falls 4.9 m after 1.0 s has elapsed. How
much farther does it drop in the next 2.0 seconds? (a) 9.8 m (b) 19.6 m (c) 39 m (d) 44 m (e) 27 m
y3  v 0 t 
1 2
1
2
at  0 
9.8 m s2  3.0 s   44 m
2
2


 y  y3  y1  44 m  4.9 m  39 m
7. An object moves along the x-axis, its position measured at each instant of time. The data are
organized into an accurate graph of x vs. t. Which of the following quantities cannot be obtained from
this graph? (a) the velocity at any instant (b) the acceleration at any instant (c) the displacement during
some time interval (d) the average velocity during some time interval (e) the speed of the particle at any
instant
8. People become uncomfortable in an elevator if it accelerates from rest at a rate such that it attains a
speed of about 6 m/s after descending ten stories (about 30 m). What is the approximate magnitude of its
acceleration? (Choose the closest answer.) (a) 10 m/s2 (b) 0.3 m/s2 (c) 0.6 m/s2 (d) 1 m/s2 (e) 0.8 m/s2
v 2  v 02
 6 m s   0  0.6 m s2
a 

2   y
2  30 m 
2
9. Races are timed to an accuracy of 1/1 000 of a second. What distance could a person rollerblading at a
speed of 8.5 m/s travel in that period of time? (a) 85 mm (b) 85 cm (c) 8.5 m (d) 8.5 mm (e) 8.5 km


 x  v   t    8.5 m s  1.0  10 3 s  8.5  10 3 m  8.5 mm
10. A student at the top of a building throws a red ball upward with speed v0 and then throws a blue ball
downward with the same initial speed v0. Immediately before the two balls reach the ground, which of
the following statements are true? (Choose all correct statements; neglect air friction.) (a) The speed of
the red ball is less than that of the blue ball. (b) The speed of the red ball is greater than that of the blue
ball. (c) Their velocities are equal. (d) The speed of each ball is greater than v0 (e) The acceleration of
the blue ball is greater than that of the red ball.
11. A rock is thrown downward from the top of a 40.0 m tower with an initial speed of 12 m/s.
Assuming negligible air resistance, what is the speed of the rock just before hitting the ground? (a) 28
m/s (b) 30 m/s (c) 56 m/s (d) 784 m/s (e) More information is needed.
v   v02  2a  y  
v02  2   g   h  
12

m s   2 9.8 m s2
2
  40.0 m   30 m s
12. A ball is thrown straight up in the air. For which situation are both the instantaneous velocity and the
acceleration zero? (a) on the way up (b) at the top of the flight path (c) on the way down (d) halfway up
and halfway down (e) none of these
2
PHYS-1401: College Physics-I
CRN 55178
Khalid Bukhari
HW-2
13. If the velocity of a particle is nonzero, can the particle’s acceleration be zero?
a) yes b) No
14. If the velocity of a particle is zero, can the particle’s acceleration be zero?
a) yes b) No
15. If a car is traveling eastward, can its acceleration be westward?
a) yes b) No
16. Can the equations of kinematics be used in a situation where the acceleration varies with time?
a) yes b) No
17. Can the instantaneous velocity of an object at an instant of time ever be greater in magnitude than
the average velocity over a time interval containing that instant?
a) yes b) No
18. A ball is thrown vertically upward. (a) What are its velocity and acceleration when it reaches its
maximum altitude?
a) v = max a = 0 b) v = max a = -9.8 m/s2 c) v = 0, a = -9.8 m/s2
3
PHYS-1401: College Physics-I
CRN 55178
Khalid Bukhari
HW-2
PART-B: Hand in your solutions to the following questions in class, on Wednesday 19 September-2010.
Show the detailed calculations. Write your final answers in the box.
1.
A person travels by car from one city to another with different constant speeds between pairs of
cities. She drives for 30.0 min at 80.0 km/h, 12.0 min at 100 km/h, and 45.0 min at 40.0 km/h and
spends 15.0 min eating lunch and buying gas. (a) Determine the average speed for the trip. (b)
Determine the distance between the initial and final cities along the route.
 x1 = v1   t1
   80.0 km h   0.500 h   40.0 km
 x2 = v 2   t2   100 km h   0.200 h   20.0 km
 x3 = v3   t3    40.0 km h   0.750 h   30.0 km
Thus, the total distance traveled x = (40.0 + 20.0 + 30.0) km = 90.0 km, and the elapsed time is
t = 0.500 h + 0.200 + 0.750 h + 0.250 h = 1.70 h).
2.
A motorist drives north for 35.0 minutes at 85.0 km/h and then stops for 15.0 minutes. He then
continues north, traveling 130 km in 2.00 h. (a) What is his total displacement? (b) What is his
average velocity?
(a)
 1h 
Displacement   x   85.0 km h   35.0 min  
 130 km  180 km
 60.0 min 
(b) The total elapsed time is
 1h 
t   35.0 min  15.0 min  
 2.00 h  2.84 h
 60.0 min 
so, v 
x
180 km

 63.4 km h
t
2.84 h
3.
A Cessna aircraft has a liftoff speed of 120 km/h. (a) What minimum constant acceleration does
the aircraft require if it is to be airborne after a takeoff run of 240 m? (b) How long does it take the
aircraft to become airborne?
(a)
With v  120 km h , v2  v02  2a  x  yields
a 
(b)
4
v2  v02
2  x
  120 km h 2  0 
2

  0.278 m s   2.32m/s2
 
 1 km h 
2  240 m 
The required time is  t 
v  v0
120 km h  0   0.278 m s   14.4 s

.
 1 km h 
a
2 .32 m s2
A certain freely falling object requires 1.50 s to travel the last 30.0 m before it hits the ground.
From what height above the ground did it fall?
The velocity of the object when it was 30.0 m above the ground can be determined by applying
y  v0 t  21 at 2 to the last 1.50 s of the fall. This gives
30.0 m  v0  1.50 s  
1
m
2
9.80 2   1.50 s 

2
s 
or
v0  12.7 m s
The displacement the object must have undergone, starting from rest, to achieve this velocity at
a point 30.0 m above the ground is given by v2  v02  2a  y  as
4
PHYS-1401: College Physics-I
 y 1
CRN 55178
Khalid Bukhari
HW-2
v2  v02
 12.7 m s   0  8.23 m

2a
2 9.80 m s2
2



The total distance the object drops during the fall is
 y total
5.

 y 1   30.0 m 
 38.2 m
A small mailbag is released from a helicopter that is descending steadily at 1.50 m/s. After 2.00
s, (a) what is the speed of the mailbag, and (b) how far is it below the helicopter? (c) What are your
answers to parts (a) and (b) if the helicopter is rising steadily at 1.50 m/s?
(a) After 2.00 s, the velocity of the mailbag is

vbag  v0  at  1.50 m s  9.80 m s2
  2 .00 s    21.1 m s
The negative sign tells that the bag is moving downward and the magnitude of the velocity
gives the speed as 21.1 m/s.
(b) The displacement of the mailbag after 2.00 s is
 y bag
 21.1 m s   1.50 m s  
 v  v0 
 
t  
  2 .00 s    22 .6 m

 2 
2


During this time, the helicopter, moving downward with constant velocity, undergoes a displacement of
 y copter
 v0 t 
1 2
at   1.5 m s   2 .00 s   0   3.00 m
2
The distance separating the package and the helicopter at this time is then
d 
 y  p   y  h
 22.6 m   3.00 m   19.6 m  19.6 m
(c) Here,  v0 bag   v0 copter   1.50 m s and abag  9.80 m s2 while acopter = 0. After 2.00 s,
the velocity of the mailbag is
vbag  1.50
m 
m
m
  9.80 2   2.00 s    18.1
s
s


s
and its speed is
vbag  18.1
m
s
In this case, the displacement of the helicopter during the 2.00 s interval is
ycopter   1.50 m s   2.00 s   0  3.00 m
Meanwhile, the mailbag has a displacement of
 y bag
 vbag  v0 
 18.1 m s  1.50 m s 
 
t  

  2 .00 s   16.6 m
2
2




The distance separating the package and the helicopter at this time is then
d 
 y  p   y  h
 16.6 m   3.00 m   19.6 m  19.6 m
5