Motion in Straight Line PW
Motion in Straight Line PW
ssessment iscomplementary part of the learning process. It gives you atotal insight whether the learning outcomes
Ahave been achieved or not. After going through the corresponding NCERT Textbookchapter, atternpt these questiont
in exam like environment. Give yourself four marks for correct answer and deduct one mark for wrong answer. Atable
is given at the end, that willhelp you plan your next step.
Alithe Best!
(d) Displacement does not tell the nature of the (a) The average speed of the car in going
actual motion of aparticle between the points. Oto Pand come back to Q is 20 ms.
5. If a man goes 10 m toward north and 20 m toward (b) The average velocity of the car in going trom
east, then hisdisplacement is to P and come back to O is 10 ms. from
(a) 22.5 m (b) 25 m (c) 25.5 m (d) 30 m (c) The average speed of the car in going
to Pand come back to O is 20 ms. from 0
O
6. Adrunkard is walking along a straight road. He
takes 5 steps forward and 3 steps backward and so (d) The average velocity of the car in going
to Pand come back to O is 20 ms.
on. Each step is Im long and takes 1s. There is a
Physics | Motion in a Straight Line 33
10. The area under velocity-time graph for a particle in (a) Its speed is zero.
a given interval of time represents (b) Its acceleration is zero.
(a) velocity (b) acceleration
(c) work done
(c) Its acceleration is opposite to the velocity.
(d) displacement (d) Its speed may be variable.
11. Acyclist moving on a circular track of radius 19. The position of an object moving along x-axis is
40m conmpletes half a revolution in 40s. Its average given by x=a+bt', where a= 8.5 m and b= 2.5 ms
velocity is (in ms')
(a) zero (b) 4T (c) 2
and t is measured in seconds. The instantaneous
(d) 8 velocity (in ms) of the object at t = 2 s is
12. The position of an object moving along x-axis is (a) 5 (b) 10 (c) 15 (d) 20
given by x=a+bt, where a=8.5 m and b= 2.5 ms-2
and tis measured in seconds. The average velocity of 20. The motion of aparticle is described by the equation
the object between t= 2 s and t= 4 s is x= at +bt, where a= 15 cm s andb=3 cm s.
(a) 5 ms-! Its instantaneous velocity(in cm s) at t= 3 swill be
(b) 10 m s (a) 33 (b) 18 (c) 16 (d) 32
(c) 15 m s! (d) 20 ms
13. Which of the following graphs represents the 21. The motion of a particle is described by
position-time graph of a particle moving with x =x(1 - e); t> 0, x, >0, k > 0., With what
negative velocity? velocity does the particle start?
(a)
k
(b) xok (c) (d) 2xgk
(a) (b) 22. The velocity of the particle at any time t is given by
v= 2(3 - ) ms. At what time is its velocity
maximum?
2 3
(a) 2s (b) 3s (c) =s (d)
3 2
(c) (d) 23. The motion of a body is given by the equation
dv
dt
=6-3v where v is the speed in m s and t is
14. Abody moving along a straight line travels one
third of the total distance witha speed of 3.0 ms. time in s. The body is at rest at t = 0. The speed
varies with time as
The remaining distance is covered with a speed of
4.0 msfor half the time and 5.0 msfor the other (a) v=(|-e) (b) v= 2(1 -e)
(c) v= (1+e) (d) v=2(1 +e)
half of the time. The average speed (in ms ' during
the motion is 24. The position x of a particle with respect to time t
(a) 4.0 (b) 6.0 (c) 3.8 (d) 2.4 along x-axis is given by x =9t-twhere x is in metres
15. Aboy walks on a straight road from his home to a and t is in seconds. What will be the position of this
market 2.5 km with a speed of 5 km h. Finding particle when it achieves maximum speed along the
the market closed he instantly turns and walks back tx direction ?
with aspeed of 7.5 km h'. What is the average (a) 54 m (b) 81 m (c) 24 m (d) 32 m
speed and average velocity of the boy between 25. Figure shows the displacement(x)-time (t) graph of
t=0 to t= 50 min? a particle moving on the x-axis.
(a) 0,0 (b) 6 kmh',0 (a) The particle is at rest.
(c) 0,6 km hl (d) 6 kmh-', 6 km h-! (b) The particle is continuously
going along x-direction.
34 Instantaneous Velocity and Speed (c) The velocity of the particle
16. Speedometer of a car measures
increases upto time t, and then becomes
constant.
(a) average speed (b) average velocity (d) The particle moves at a constant velocity up to
(C) instantaneous speed (d) instantaneous velocity a time to and then stops.
17. Speedometer measures the speed of the car in 26. Figure shows the x-t plot of a particle in one
(a) ms (b) km hl dimensional motion. Two
(c) cms (d) km min! different equal intervals of time
IH, Aparticle moves with uniform velocity. Which of are shown. Let v, and v, be
the following statements about the motion of the average speed in time intervals
particle is true? land 2 respectively. Then
34 wtG objective NCERT at your Fingertos
(a) v;> v: (a) () and (ii) (b) (ii) and (ii)
(c) V= V; (d) data is insufficient (c) (), (ii) and (iii) (d) All four
27. The position-time (r-t) graphs
for two children Aand B 33 Acceleration
returning from their school O 32. The displacement of a body is given to be
P
to their homes P and Q proportional to the cube of time elapsed. The
respectively are as shown in the magnitude of the acceleration of the body is
figure. Choose the incorrect (a) increasing with time
statement regarding these graphs. (b) decreasing with time
(a) Alives closer to the school than B. (c) constant but not zero
(d) zero.
(b) A starts from the school earlier than B.
(c) A walks faster than B. 33. Match the Column Iwith Column II.
(a) A-p, B- q, C- s, D -r X
(b) A- q, B- p, C-r,D - s
(c) A - s, B - r, C-4, D -p
(c) (d)
(d) A-r, B- q, C- s, D - p
38. Aparticle moving along a straight line has avelocity
vms,when it cleared a distance of x m. These two 45. The velocity-displacement graph of a particle is as
are connected by the relation v=y49+x. When its shown in the figure.
velocity is 1ms, its acceleration (in ms) is Which of the following graphs V'o
(a) 2 (b) 7 (c) 1 (d) 0.5 correctly represents the variation
39. A particle moves rectilinearly. Its displacenment x of acceleration with displacement?
at time t is given by x=at' + b where a and b are
constants. Its acceleration at time tis proportional
to
(a) (b)
1 t 1
(a) (b) (d)
X x
40. A car starts from rest, attains a velocity of 36 km h'
with an acceleration of 0.2 ms, travels 9 km with
this uniform velocity and then comes to halt with
a uniform deceleration of 0.1 m s,The total time (c) (d)
of travel of the car is
(a) 1050s (b) 1000 s (c) 950 s (d) 900 s
1. A particle moving with uniform acceleration has
average velocities V,, V, and v, over the successive 46. The velocity-time graph of a v
intervals of time t,, t, and t,respectively. The value particle in one-dinmensional
motion is shown in the figure.
of willbe Which of the following
(, - v,) formulae is correct for )
(a) - (b) 1 describing the motion of the
t-ls particle over the tinme interval,to ,?
36 mtG Objective NCERT at your
Fingertips
(a) >O> (b)
(a) x(t,) =x() + v(t,) (; - t) +) alt, - t)' (d) ):
(c) O>>
(b) v(t) = v(t;) + a(t, - t,)
(c) Vaverage (x(t,)+ x()) 3.6 Kinematic Equations for
(t,-,)
Uniformly Accelerated Motion
(d) average
(v(t,)- v(t, ) 51. Abody starts from rest and moves with
(t, - ) acceleration for ts. It travels a distance x, constant
in fr.
47. Givenbelow are four curves describingvariation of half of time andx, in next half of time, then
velocity with time of a particle. Which one of these (a) x, = 3x1 (b) x, = X|
describe the motion of a particle initially in positive (c) x, = 4x1 (d) x, = 2x1
direction withconstant negative acceleration?
52. Free fall of an object in vacuum is a case of motion
with
(a) uniform velocity (b) uniform acceleration
(a) (b) (c) variable acceleration (d) uniform speed
53. Which of the following equations does not represent
the kinematic equations of motion ?
(a) v =u+ at (b) S= ut +at
2
(c) (d) (c) S=vt +-at? (d) y²- u'=2aS
2
54. Which of the following statements is not correct?
48. The speed-time graph of Speed(msl)
(a) The zero velocity of a body at any instant does
a particle moving along not necessarily imply zero acceleration at that
instant.
a fixed direction is
shown in the figure. The 12 (b) The kinematic equation of motions are true
distance travelled by the only for motion in which the magnitude and
the direction of acceleration are constants
particle between t = 2 s
to t = 6 s is
5 10 Time (s) during the course of motion.
(a) 26 m (b) 36 m (c) 46 m (d) 56 m (c) The sign of acceleration tells us whether the
particle's speed is increasing or decreasing.
49. The given acceleration-time graph represents which (d) All of these
of the following physical situations? 55. The distances covered by a freely falling body in its
a
first, second, third,. ,nh seconds of its motion
(a) forms an arithmetic progression
(b) forms a geonetric progression
(c) do not form any well defined series
(d) form a series correspondinggto the diferenceof
(a) A cricket ball moving with auniform speed is Square root of the successive naturalnumbers.
hit with a bat for a very short time interval.
(b) A ball is falling freely from the top of a tower. 56. Abody covers 20 m, 22 m, 24 m, in 8th gth and
(c) A car moving with constant velocity on a seconds respectively. The body starts
straight road. (a) from rest and moves with uniform velocy acceleration
(d) A football is kicked into the air vertically (b) from rest and moves with uniform: uniform
upwards. (c) with an initial velocity and moves with
acceleration uniform
50. The figure shows a particle (d) with an initial velocity and moves with
moving along x-axis 4(vs) 8 f
6
velocity.
subjected to three intervals 4
(c) the velocity of theball is zero but its acceleration one-fourth the distance starting from rest at the
is g top?
(d) the velocity of the ball is u but its acceleration (a) Is (b) 4 s (c) 2s (d) 16s
is g.
67. A ball is thrown vertically upwards with a
58. A car moving along a straight road with speed of velocity of 20 m s from the top of a multistorey
144 km h is brought to astop within adistance of building of 25 m high. How high will the ball rise?
200m. How long does it take for the car to stop? (Takeg = 10m s )
(a) 5s (b) 10s (c) 15 s (d) 20 s (a) 10 m (b) 15 m (c) 20 m (d) 25 m
59. An auto travelling along a straight road increases 68. In thequestion number 67, the time taken by the
itsspeed from30.0 m sto S0.0 m s in a distance ball to reach the ground is
of 180 m. If the acceleration is constant, how much (a) 2 s (b) 3 s (c) 5 s (d) 7s
time elapses while the auto moves this distance?
(a) 6.0s (b) 4.5 s (c) 3.6s (d) 7.0 s 69. Two trains A and B each of length 400 m are
moving on two parallel tracks with a uniform speed
60. Abody falling freely under gravity passes two points 72 km h' in the same direction with A ahead
30 m apart in ls. From what point above the upper of B. The driver of B decides to overtake A and
point it began to fall? (Take g=9.8 m s). accelerates by l m s. If after 50 s, the guard of B
(a) 32.1 m (b) l6.0 m (c) 8.6 m (d) 4.0 m just brushes past A, what was the original distance
61. A player throws a ball upwards with an initial speed (in m) between them?
of 30 m s. How long does the ball take to return (a) 750 (b) 1000 (c) 1250 (d) 2250
to the player's hands? (Take g = 10 m s2)
(a) 3 s (b) 6s (c) 9s (d) 12 s 70. The velocity of aparticle at an instant is 10 ms.
After 3 s its velocity will become 16 ms'. The
62. Agirl standing on astationary lift (open from above) velocity (in ms)at 2 s, before the given instant will be
throws a ball upwards with initial speed 50 m s-!, (a) 6 (b) 4 (c) 2 (d) 1
The time taken by the ball to return to her hands is
(Take g= 10 m s) 71. A body covers a distance of 4 m in 3rd second and
12 m in 5h second. If the motion is uniformly
(a) 5s (b) 10 s (c) 15 s (d) 20 s
accelerated, how far will it travel in the next
63. In the question number 62, if the lift starts moving 3 seconds?
up with a uniform speed of 5 m s and the girl (a) 10 m (b) 30 m (c) 40 m (d) 60 m
again throws the ball up with the same speed, how
long does the ball take to return to her hands? 72. Stopping distance of a moving vehicle is directly
(a) 5 s (b) 10 s (c) 15 s (d) 20 s proportional to
(a) square of the initial velocity
64. It is a common observation that rain clouds can be
(b) square of the initial acceleration
at about 1 km altitude above the ground. If a rain (c) the initial velocity
drop falls from such a height freely under gravity, (d) the initial acceleration
then what will be its speed in km h?
(Take g = 10 m s) 73. A car moving with a speed of 50 km h' can be
(a) 510 (b) 610 (c) 710 (d) 910 stopped by applying brakes after moving atleast 6 m.
65. Aman is standing on top of a building 100 m high. If the same car is moving at a speed of 100 km h, the
minimum stopping distance is
He throws two balls vertically upwards, one at t= (a) 6 m (b) 12 m (c) 18 m (d) 24 m
Oand other after a time interval (less than 2 s). The
later ball is thrown at a velocity of half the first. 74. An object falling through a fluid is observed
Ihe vertical gap between first and second ball is 15 to have acceleration given by a= g -bv where
m at t = 2 s. The gap is found to remain constant. g= gravitational acceleration and b is constant.
The velocities with which the balls were thrown are After along time of release, it is observed to fall
(Take g = 10 m s) with constant speed. The value of constant speed is
(a) 20 m s ,10 ms! (b) 10ms,5 m s-! (a) &
(c) 16 ms,8 ms! (b) (c) bg (d) b
(d) 30 m s ,15 m s
00. Abody sliding on asmooth inclined plane requires 75. A particle is released from rest from a tower of
4 seconds to reach the bottom, starting from rest height 3h. The ratio of the intervals of time to cover
at the top. How much time does it take to cover three equal heights h is
38 mtG Objective NCERI at your Fingertins
-1
(a) t: t: t = 3: 2:1 15 m s and 30 ms respectively. The time
(b) t,:t:t, =l: (V2-1):(V3-2) variation of the relative position of the second stom
with respect to the x-x,(m)
(c) t:t :ty = V3:N2:1 first is shown in
120
(d) 4:t,:t, =l:(V2-1):(V3-V2) the figure. The 100
76. A stone is dropped from the top of a tall cliff and equation of the 80
(a)
2
(b) 8 3.7 Relative Velocity
2 (u-gn) 2 (u-gn)
83. Aball Ais dropped from a building of height 45 m.
-gn Simultaneously another identical ball Bis thrown up
bol g (u-gn) with aspeed 50 ms.The relative speed (in ms)of
(d)
-gn 5\||gn ball Bw.r.t. ball Aat any instant of time is
(Take g 10 m s)
77. A motorcycle and a car start from rest from the (a) 0 (b) 10 (c) 25 (d) 50
same place at the same time and travel in the same 84. A ball Ais thrown vertically upwards with speed u.
direction. The motorcycle accelerates at 1.0 m s up At the same instant another ball Bis released from
to aspeed of 36 km h and the car at 0.5 m s up to a rest at height h. At time t, the speed of A relative to
speed of 54 km h. The time at which the car would Bis
overtake the motorcycle is (a) u (b) u - 2gt
(a) 20 s (b) 25 s (c) 30 s (d) 35 s
(c) Ju'-2gh (d) u -gt
78. A body initially at rest is moving with uniform 85. Two cars A and Bare running at velocities of
acceleration a. Its velocity after n seconds is v. The 60 km h' and 45 km h-!. What is the relative
displacement of the body in last 2 s is velocity (in km h)of car A with respect to car B,
(a) 2v(n-1) v(n-1)
(b)
if both are moving eastward?
(a) 15 (b) 45 (c) 60 (d) 105
v(n+1) 2v(n+1) 86. In question number 85,what is the relative velocity
(c) (d)
n (in km h') of a car A with respect to car B, if car A
79. A body A starts from rest with an acceleration a,.
ismoving eastward and car B is moving westward'
After 2 seconds, another body B starts from rest (a) 15 (b) 45 (c) 60 (d) 105
with an acceleration a,. If they travel equal distances
in the 5" second, after the start ofA, then the ratio 87. Ona two-lane road, car A is travelling with a speed
of 36 km h. Two cars B and Capproach ar A
a, :a, is equal to opposite directions with a speed of 54 km h' each.
(a) 5:9 (b) 5:7 (c) 9:5 (d) 9:7
80. A bullet fired into a wooden block loses At acertain instant, when thedistance AB is equa
half of its to AC, both being l km, B decides to overtake A
velocity after penetrating 40 cm. It comes to rest before Cdoes. The minimum required acceleration
after penetrating a further distance of (in m s) of car B to avoid an accident is
22 40 20
(a) 22 (a) 1 (d) 3
3 cm (b) cm (c) (b) 1.5
3 cm (d) 5 cm (c) 2
81. A body moving with some initial velocity and 88. Abird is tossing (flying to and fro) between two cars
One
having uniform acceleration attains a final velocity moving towards each other on a straight road.
vm/s after travelling x m. If its final velocity is car has speed of 27 km h- while the other has first
v= J180 -
7x, find the acceleration (in m/s) of speed of18 km h, The bird starts moving from
the body. car towards the other theespeedof
36 km h when theand is cars
two 3 with
movingwere separated by
(a) -3.5 (b) -7 (c) - 15 (d) - 30 36 km. The total distance (in covered bythe
82. Two stones are thrown up simultaneously from km)
bird is
the edge of a cliff 200 m high with initial speeds of (a) 28.8 (d) 58.8
(b) 38.8 (c) 48.8
Physics | Motion in a Straight Line 39
89. A police van moving on a highway with a speed 95. Atrain A which is 120 m long is running with
of 30 kmh fires a bullet at a thief's car speeding velocity 20 m/s while train B which is 130 m long
away in the same direction with a speed of is running in opposite direction with velocity
192 km h. If the muzzle speed of the bullet is 150 30 m/s. What is the time taken by train B to cross
ms, with what speed (in ms) does the bullet hit the train A?
the thief's car?
(a) 5 s (b) 25 s (c) 10 s (d) 100 s
(a) 95 (b) 105 (c) 115
(d) 125
96. A jet airplane travelling at the speed of 500 km h'
90. A bus is moving with a speed of 10 m s on a ejects its products of combustion at the speed of
straight road. A scooterist wishes to overtake the 1500 km h relative to the jet plane. The speed
bus in 100 s. If the bus is at a distance of 1km from (in km h) of the products of combustion with
the scooterist with what speed (in ms )should the respect to an observer on the ground is
scooterist chase the bus? (a) 500 (b) 1000 (c) 1500 (d) 2000
(a) 40 (b) 25 (c) 10 (d) 20 97. On a long horizontally moving belt, a child runs to
91. Two towns A and B are connected by a regular bus and fro with a speed9 kmh' (with respect to the belt)
service with abus leaving in either direction every between his father and mother located 50 m apart
Tminutes. Aman cycling with a speed of 20 km hl on the moving belt. The belt moves with a speed of
in the direction A to B notices that a bus goes past 4 km h. For an observer on a stationary platform,
him every 18 min in the direction of his motion, the speed (in km h) of the child running in the
and every 6 min in the opposite direction. The direction of motion of the belt is
time period T of the bus service is (a) 4 (b) 5 (c) 9 (d) 13
(a) 4.5 min(b) 9 min (c) 12 min (d) 24 min 98. In the question number 97, thespeed (in kmh)of the
92. A175 mlong train is traveling along a straight track child running opposite to the direction of motion of the
belt is
with a velocity 72 km h. A bird is flying parallel (a) 4 (b) 5 (c) 9
to the train in the opposite direction with a velocity (d) 13
18 kmh. The time taken by the bird to cross the 99. In the question number 97,time taken by the child
train is to go from father to mother and back to father is
(a) 35 s (b) 27 s (c) 11.6 s (d) 7 s (a) 10 s
(b) 20 s (c) 30 s (d) 40 s
100.Which one of the following represents
93. Two parallel rail tracks run north-south. On
one track train A moves north with a speed
of 54 kmh' and on the other track train B moves
south with aspeed of 90 km h-. The velocity
(in ms )of train Awith respect to train B is (a)
Displacemnt
displacement-time graph of two objects A and B
moving with zero relative velocity?
4
B (b)
Displacemnt 1
B
B
(d)
Displacemnt Time