Motion in a Straight Line- 1 Practice Questions - DPP for NEET

 Page 1


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A particle moving in a straight line covers half the distance
with speed of 3 m/s. The other half of the distance is
covered in two equal time intervals with speed of 4.5 m/s
and 7.5 m/s respectively. The average speed of the particle
during this motion is
(a) 4.0 m/s (b) 5.0 m/s
(c) 5.5 m/s (d) 4.8 m/s
Q.2 The acceleration of a particle is increasing linearly with
time t as bt. The particle starts from the origin with an initial
velocity v
0
.
 
The distance travelled by the particle in time t
will be
(a)
2
0
1
3
v t bt +
(b)
3
0
1
3
v t bt +
(c)
3
0
1
6
v t bt +
(d)
2
0
1
2
v t bt +
Q.3 The motion of a body is given by the equation
()
6.0 3 ( ), =-
dvt
vt
dt
 where v(t) is speed in m/s and t in sec.
If body was at rest at t = 0
(a) The terminal speed is 4 m/s
(b) The speed varies with the time as v(t) = 2(1 – e
–5t
)m/s
(c) The speed is 0.1m/s when the acceleration is half the
initial value
(d) The magnitude of the initial acceleration is 6.0 m/s
2
Page 2


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A particle moving in a straight line covers half the distance
with speed of 3 m/s. The other half of the distance is
covered in two equal time intervals with speed of 4.5 m/s
and 7.5 m/s respectively. The average speed of the particle
during this motion is
(a) 4.0 m/s (b) 5.0 m/s
(c) 5.5 m/s (d) 4.8 m/s
Q.2 The acceleration of a particle is increasing linearly with
time t as bt. The particle starts from the origin with an initial
velocity v
0
.
 
The distance travelled by the particle in time t
will be
(a)
2
0
1
3
v t bt +
(b)
3
0
1
3
v t bt +
(c)
3
0
1
6
v t bt +
(d)
2
0
1
2
v t bt +
Q.3 The motion of a body is given by the equation
()
6.0 3 ( ), =-
dvt
vt
dt
 where v(t) is speed in m/s and t in sec.
If body was at rest at t = 0
(a) The terminal speed is 4 m/s
(b) The speed varies with the time as v(t) = 2(1 – e
–5t
)m/s
(c) The speed is 0.1m/s when the acceleration is half the
initial value
(d) The magnitude of the initial acceleration is 6.0 m/s
2
2
DPP/ P 03
Q.4 A particle of mass m moves on the x-axis as follows: it
starts from rest at t = 0 from the point x = 0 and comes to
rest at t = 1 at the point x = 1. No other information is
available about its motion at intermediate time (0 < t < 1).
If a denotes the instantaneous acceleration of the particle,
then
(a) a cannot remain positive for all t in the interval
01 t ££
(b)| a | cannot exceed 2 at any point in its path
(c)| a | must be > 4 at some point or points in its path
(d)| a | = 2 at any point in its path.
Q.5 A particle starts from rest. Its acceleration (a) versus time
(t) graph is as shown in the figure. The maximum speed of
the particle will be
11
t (s)
10 m/s
2
a
(a) 110 m/s (b) 55 m/s
(c) 550 m/s (d) 660 m/s
Q.6 A car accelerates from rest at a constant rate a for some
time, after which it decelerates at a constant rate b  and
comes to rest. If the total time elapsed is t, then the maximum
velocity acquired by the car is
(a)
22
t
æö
a +b
ç÷
ç÷
ab
èø
(b)
22
t
æö
a -b
ç÷
ç÷
ab
èø
(c)
()t a+b
ab
(d)
t ab
a +b
Q.7 A small block slides without friction down an inclined plane
starting from rest. Let S
n
 be the distance travelled from
time t = n – 1 to t = n. Then 
1
n
n
S
S
+
is
(a)
21
2
n
n
-
(b)
21
21
n
n
+
-
(c)
21
21
n
n
-
+
(d)
2
21
n
n +
Q.8 A particle starts moving from the position of rest under a
constant acc. If it covers a distance x in t second, what
distance will it travel in next t second?
(a)x (b) 2 x (c) 3 x (d) 4 x
Q.9 What will be the ratio of the distances moved by a freely
falling body from rest in 4th and 5th seconds of journey?
(a) 4 : 5 (b) 7 : 9 (c) 16 : 25 (d) 1 : 1
Q.10If a ball is thrown vertically upwards with speed u, the
distance covered during the last t seconds of its ascent is
(a)  (u+gt)t (b) ut (c)
2
gt
2
1
(d) ut – 
1
2
gt
2
Q.11 If the displacement of a particle is (2t
2
 + t + 5) meter
then, what will be acc. at t = 5 second?
(a) 21 m/s
2
(b) 20 m/s
2
(c) 4 m/s
2
(d) 10 m/s
2
Q.12 A particle moves along x-axis with acceleration a = a
0
 (1 – t/
T)  where a
0
 and T are constants if velocity at t = 0 is zero
then find the average velocity from t = 0 to the time when a
= 0.
(a)
0
aT
3
(b)
0
aT
2
(c)
0
aT
4
(d)
0
aT
5
Q.13 A point moves with uniform acceleration and v
1
, v
2
 and v
3
denote the average velocities in the three successive
intervals of time t
1
, t
2
 and t
3
. Which of the following
relations is correct ?
(a) (v
1
– v
2
) : (v
2
– v
3
) = (t
1
– t
2
) : (t
2
+ t
3
)
(b) (v
1
– v
2
) : (v
2
– v
3
) = (t
1
+ t
2
) : (t
2
+ t
3
)
(c) (v
1
– v
2
) : (v
2
– v
3
) = (t
1
– t
2
) : (t
2 
– t
3
)
(d) (v
1
– v
2
) : (v
2
– v
3
) = (t
1
– t
2
) : (t
2 
– t
3
)
Q.14 The position of a particle moving in the xy-plane at any
time t is given by x = (3t
2
 – 6t) metres, y = (t
2
 – 2t) metres.
Select the correct statement about the moving particle from
the following
(a) The acceleration of the particle is zero at t = 0 second
(b) The velocity of the particle is zero at t = 0 second
(c) The velocity of the particle is zero at t = 1 second
(d) The velocity and acceleration of the particle are never
zero
Page 3


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A particle moving in a straight line covers half the distance
with speed of 3 m/s. The other half of the distance is
covered in two equal time intervals with speed of 4.5 m/s
and 7.5 m/s respectively. The average speed of the particle
during this motion is
(a) 4.0 m/s (b) 5.0 m/s
(c) 5.5 m/s (d) 4.8 m/s
Q.2 The acceleration of a particle is increasing linearly with
time t as bt. The particle starts from the origin with an initial
velocity v
0
.
 
The distance travelled by the particle in time t
will be
(a)
2
0
1
3
v t bt +
(b)
3
0
1
3
v t bt +
(c)
3
0
1
6
v t bt +
(d)
2
0
1
2
v t bt +
Q.3 The motion of a body is given by the equation
()
6.0 3 ( ), =-
dvt
vt
dt
 where v(t) is speed in m/s and t in sec.
If body was at rest at t = 0
(a) The terminal speed is 4 m/s
(b) The speed varies with the time as v(t) = 2(1 – e
–5t
)m/s
(c) The speed is 0.1m/s when the acceleration is half the
initial value
(d) The magnitude of the initial acceleration is 6.0 m/s
2
2
DPP/ P 03
Q.4 A particle of mass m moves on the x-axis as follows: it
starts from rest at t = 0 from the point x = 0 and comes to
rest at t = 1 at the point x = 1. No other information is
available about its motion at intermediate time (0 < t < 1).
If a denotes the instantaneous acceleration of the particle,
then
(a) a cannot remain positive for all t in the interval
01 t ££
(b)| a | cannot exceed 2 at any point in its path
(c)| a | must be > 4 at some point or points in its path
(d)| a | = 2 at any point in its path.
Q.5 A particle starts from rest. Its acceleration (a) versus time
(t) graph is as shown in the figure. The maximum speed of
the particle will be
11
t (s)
10 m/s
2
a
(a) 110 m/s (b) 55 m/s
(c) 550 m/s (d) 660 m/s
Q.6 A car accelerates from rest at a constant rate a for some
time, after which it decelerates at a constant rate b  and
comes to rest. If the total time elapsed is t, then the maximum
velocity acquired by the car is
(a)
22
t
æö
a +b
ç÷
ç÷
ab
èø
(b)
22
t
æö
a -b
ç÷
ç÷
ab
èø
(c)
()t a+b
ab
(d)
t ab
a +b
Q.7 A small block slides without friction down an inclined plane
starting from rest. Let S
n
 be the distance travelled from
time t = n – 1 to t = n. Then 
1
n
n
S
S
+
is
(a)
21
2
n
n
-
(b)
21
21
n
n
+
-
(c)
21
21
n
n
-
+
(d)
2
21
n
n +
Q.8 A particle starts moving from the position of rest under a
constant acc. If it covers a distance x in t second, what
distance will it travel in next t second?
(a)x (b) 2 x (c) 3 x (d) 4 x
Q.9 What will be the ratio of the distances moved by a freely
falling body from rest in 4th and 5th seconds of journey?
(a) 4 : 5 (b) 7 : 9 (c) 16 : 25 (d) 1 : 1
Q.10If a ball is thrown vertically upwards with speed u, the
distance covered during the last t seconds of its ascent is
(a)  (u+gt)t (b) ut (c)
2
gt
2
1
(d) ut – 
1
2
gt
2
Q.11 If the displacement of a particle is (2t
2
 + t + 5) meter
then, what will be acc. at t = 5 second?
(a) 21 m/s
2
(b) 20 m/s
2
(c) 4 m/s
2
(d) 10 m/s
2
Q.12 A particle moves along x-axis with acceleration a = a
0
 (1 – t/
T)  where a
0
 and T are constants if velocity at t = 0 is zero
then find the average velocity from t = 0 to the time when a
= 0.
(a)
0
aT
3
(b)
0
aT
2
(c)
0
aT
4
(d)
0
aT
5
Q.13 A point moves with uniform acceleration and v
1
, v
2
 and v
3
denote the average velocities in the three successive
intervals of time t
1
, t
2
 and t
3
. Which of the following
relations is correct ?
(a) (v
1
– v
2
) : (v
2
– v
3
) = (t
1
– t
2
) : (t
2
+ t
3
)
(b) (v
1
– v
2
) : (v
2
– v
3
) = (t
1
+ t
2
) : (t
2
+ t
3
)
(c) (v
1
– v
2
) : (v
2
– v
3
) = (t
1
– t
2
) : (t
2 
– t
3
)
(d) (v
1
– v
2
) : (v
2
– v
3
) = (t
1
– t
2
) : (t
2 
– t
3
)
Q.14 The position of a particle moving in the xy-plane at any
time t is given by x = (3t
2
 – 6t) metres, y = (t
2
 – 2t) metres.
Select the correct statement about the moving particle from
the following
(a) The acceleration of the particle is zero at t = 0 second
(b) The velocity of the particle is zero at t = 0 second
(c) The velocity of the particle is zero at t = 1 second
(d) The velocity and acceleration of the particle are never
zero
DPP/ P 03
3
Q.15 Two cars A and B are travelling in the same direction with
velocities v
1 
and v
2
 (v
1
 > v
2
). When the car A is at a distance
d ahead of the car B, the driver of the car A applied the
brake producing a uniform retardation a. There will be no
collision when
(a)
2
12
()
2
vv
d
a
-
< (b)
22
12
2
vv
d
a
-
<
(c)
2
12
()
2
vv
d
a
-
> (d)
22
12
2
vv
d
a
-
>
Q.16A body travels for 15 second starting from rest with
constant acceleration. If it travels distances S
1
, S
2
 and S
3
in the first five seconds, second five seconds and next five
seconds respectively the relation between S
1
, S
2
 and S
3
 is
(a)S
1
 = S
2
 = S
3
(b) 5S
1
 = 3S
2
 = S
3
(c)
1 23
11
S SS
35
== (d) 1 23
11
S SS
53
==
Q.17 The position of a particle moving along the x-axis at certain
times is given below
() 0 1 23
() 206 16
ts
xm -
Which of the following describes the motion correctly?
(a) Uniform, accelerated
(b) Uniform, decelerated
(c) Non-uniform, accelerated
(d) There is not enough data for generalization
Q.18A body A moves with a uniform acceleration a and zero
initial velocity . Another body B, starts from the same point
moves in the same direction with a constant velocity v. The
two bodies meet after a time t. The value of t is
(a)
2v
a
(b)
v
a
(c)
2
v
a
(d)
2
v
a
Q.19 A particle moves along x-axis as x = 4 (t – 2) + a (t – 2)
2
Which of the following is true?
(a) The initial velocity of particle is 4
(b) The acceleration of particle is 2a
(c) The particle is at origin at t = 0
(d) None of these
Q.20The displacement x of a particle varies with time t,
x = ae
–at
 + be
bt
, where a, b, a and b are positive constants.
The velocity of the particle will
(a) Go on decreasing with time
(b) Be independent of a and b
(c) Drop to zero when a = b
(d) Go on increasing with time
DIRECTIONS (Q.21-Q.23) : In the following questions,
more than one of the answers  given are correct. Select
the correct answers and mark it according to the following
codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.21A particle moves as such acceleration is given by
a = 3 sin 4t, then :
(1) the acceleration of the particle becomes zero after
each interval of 
4
p
 second
(2) the initial velocity of the particle must be zero
(3) the particle comes at its initial position after sometime
(4) the particle must move on a circular path
Q.22 A reference frame attached to the earth :
(1) is an inertial frame by definition
(2) cannot be an inertial frame because the earth is
revolving round the sun
(3) is an inertial frame because Newton’s laws are
applicable in this frame
(4) cannot be an inertial frame because the earth is
rotating about its own axis
Page 4


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A particle moving in a straight line covers half the distance
with speed of 3 m/s. The other half of the distance is
covered in two equal time intervals with speed of 4.5 m/s
and 7.5 m/s respectively. The average speed of the particle
during this motion is
(a) 4.0 m/s (b) 5.0 m/s
(c) 5.5 m/s (d) 4.8 m/s
Q.2 The acceleration of a particle is increasing linearly with
time t as bt. The particle starts from the origin with an initial
velocity v
0
.
 
The distance travelled by the particle in time t
will be
(a)
2
0
1
3
v t bt +
(b)
3
0
1
3
v t bt +
(c)
3
0
1
6
v t bt +
(d)
2
0
1
2
v t bt +
Q.3 The motion of a body is given by the equation
()
6.0 3 ( ), =-
dvt
vt
dt
 where v(t) is speed in m/s and t in sec.
If body was at rest at t = 0
(a) The terminal speed is 4 m/s
(b) The speed varies with the time as v(t) = 2(1 – e
–5t
)m/s
(c) The speed is 0.1m/s when the acceleration is half the
initial value
(d) The magnitude of the initial acceleration is 6.0 m/s
2
2
DPP/ P 03
Q.4 A particle of mass m moves on the x-axis as follows: it
starts from rest at t = 0 from the point x = 0 and comes to
rest at t = 1 at the point x = 1. No other information is
available about its motion at intermediate time (0 < t < 1).
If a denotes the instantaneous acceleration of the particle,
then
(a) a cannot remain positive for all t in the interval
01 t ££
(b)| a | cannot exceed 2 at any point in its path
(c)| a | must be > 4 at some point or points in its path
(d)| a | = 2 at any point in its path.
Q.5 A particle starts from rest. Its acceleration (a) versus time
(t) graph is as shown in the figure. The maximum speed of
the particle will be
11
t (s)
10 m/s
2
a
(a) 110 m/s (b) 55 m/s
(c) 550 m/s (d) 660 m/s
Q.6 A car accelerates from rest at a constant rate a for some
time, after which it decelerates at a constant rate b  and
comes to rest. If the total time elapsed is t, then the maximum
velocity acquired by the car is
(a)
22
t
æö
a +b
ç÷
ç÷
ab
èø
(b)
22
t
æö
a -b
ç÷
ç÷
ab
èø
(c)
()t a+b
ab
(d)
t ab
a +b
Q.7 A small block slides without friction down an inclined plane
starting from rest. Let S
n
 be the distance travelled from
time t = n – 1 to t = n. Then 
1
n
n
S
S
+
is
(a)
21
2
n
n
-
(b)
21
21
n
n
+
-
(c)
21
21
n
n
-
+
(d)
2
21
n
n +
Q.8 A particle starts moving from the position of rest under a
constant acc. If it covers a distance x in t second, what
distance will it travel in next t second?
(a)x (b) 2 x (c) 3 x (d) 4 x
Q.9 What will be the ratio of the distances moved by a freely
falling body from rest in 4th and 5th seconds of journey?
(a) 4 : 5 (b) 7 : 9 (c) 16 : 25 (d) 1 : 1
Q.10If a ball is thrown vertically upwards with speed u, the
distance covered during the last t seconds of its ascent is
(a)  (u+gt)t (b) ut (c)
2
gt
2
1
(d) ut – 
1
2
gt
2
Q.11 If the displacement of a particle is (2t
2
 + t + 5) meter
then, what will be acc. at t = 5 second?
(a) 21 m/s
2
(b) 20 m/s
2
(c) 4 m/s
2
(d) 10 m/s
2
Q.12 A particle moves along x-axis with acceleration a = a
0
 (1 – t/
T)  where a
0
 and T are constants if velocity at t = 0 is zero
then find the average velocity from t = 0 to the time when a
= 0.
(a)
0
aT
3
(b)
0
aT
2
(c)
0
aT
4
(d)
0
aT
5
Q.13 A point moves with uniform acceleration and v
1
, v
2
 and v
3
denote the average velocities in the three successive
intervals of time t
1
, t
2
 and t
3
. Which of the following
relations is correct ?
(a) (v
1
– v
2
) : (v
2
– v
3
) = (t
1
– t
2
) : (t
2
+ t
3
)
(b) (v
1
– v
2
) : (v
2
– v
3
) = (t
1
+ t
2
) : (t
2
+ t
3
)
(c) (v
1
– v
2
) : (v
2
– v
3
) = (t
1
– t
2
) : (t
2 
– t
3
)
(d) (v
1
– v
2
) : (v
2
– v
3
) = (t
1
– t
2
) : (t
2 
– t
3
)
Q.14 The position of a particle moving in the xy-plane at any
time t is given by x = (3t
2
 – 6t) metres, y = (t
2
 – 2t) metres.
Select the correct statement about the moving particle from
the following
(a) The acceleration of the particle is zero at t = 0 second
(b) The velocity of the particle is zero at t = 0 second
(c) The velocity of the particle is zero at t = 1 second
(d) The velocity and acceleration of the particle are never
zero
DPP/ P 03
3
Q.15 Two cars A and B are travelling in the same direction with
velocities v
1 
and v
2
 (v
1
 > v
2
). When the car A is at a distance
d ahead of the car B, the driver of the car A applied the
brake producing a uniform retardation a. There will be no
collision when
(a)
2
12
()
2
vv
d
a
-
< (b)
22
12
2
vv
d
a
-
<
(c)
2
12
()
2
vv
d
a
-
> (d)
22
12
2
vv
d
a
-
>
Q.16A body travels for 15 second starting from rest with
constant acceleration. If it travels distances S
1
, S
2
 and S
3
in the first five seconds, second five seconds and next five
seconds respectively the relation between S
1
, S
2
 and S
3
 is
(a)S
1
 = S
2
 = S
3
(b) 5S
1
 = 3S
2
 = S
3
(c)
1 23
11
S SS
35
== (d) 1 23
11
S SS
53
==
Q.17 The position of a particle moving along the x-axis at certain
times is given below
() 0 1 23
() 206 16
ts
xm -
Which of the following describes the motion correctly?
(a) Uniform, accelerated
(b) Uniform, decelerated
(c) Non-uniform, accelerated
(d) There is not enough data for generalization
Q.18A body A moves with a uniform acceleration a and zero
initial velocity . Another body B, starts from the same point
moves in the same direction with a constant velocity v. The
two bodies meet after a time t. The value of t is
(a)
2v
a
(b)
v
a
(c)
2
v
a
(d)
2
v
a
Q.19 A particle moves along x-axis as x = 4 (t – 2) + a (t – 2)
2
Which of the following is true?
(a) The initial velocity of particle is 4
(b) The acceleration of particle is 2a
(c) The particle is at origin at t = 0
(d) None of these
Q.20The displacement x of a particle varies with time t,
x = ae
–at
 + be
bt
, where a, b, a and b are positive constants.
The velocity of the particle will
(a) Go on decreasing with time
(b) Be independent of a and b
(c) Drop to zero when a = b
(d) Go on increasing with time
DIRECTIONS (Q.21-Q.23) : In the following questions,
more than one of the answers  given are correct. Select
the correct answers and mark it according to the following
codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.21A particle moves as such acceleration is given by
a = 3 sin 4t, then :
(1) the acceleration of the particle becomes zero after
each interval of 
4
p
 second
(2) the initial velocity of the particle must be zero
(3) the particle comes at its initial position after sometime
(4) the particle must move on a circular path
Q.22 A reference frame attached to the earth :
(1) is an inertial frame by definition
(2) cannot be an inertial frame because the earth is
revolving round the sun
(3) is an inertial frame because Newton’s laws are
applicable in this frame
(4) cannot be an inertial frame because the earth is
rotating about its own axis
4
DPP/ P 03
Q.23 If a particle travels a linear distance at speed v
1
 and comes
back along the same track at speed v
2
.
(1) Its average speed is arithmetic mean  (v
1 
+ v
2
)/2
(2) Its average speed is harmonic mean 2 v
1
v
2
/(v
1 
+ v
2
)/2
(3) Its average speed is geometric mean 
12
vv
(4) Its average velocity is zero
DIRECTION (Q.24-Q.26) : Read the passage given below
and answer the questions that follows :
A particle moves along x-axis and its acceleration at any time t
is a = 2 sin (pt), where t is in seconds and a is in m/s
2
. The initial
velocity of particle (at time t = 0) is u = 0.
Q.24. The distance travelled (in meters) by the particle from
time to t = 0 to t = 1s will be –
(a)
2
p
(b)
1
p
(c)
4
p
(d) None  of these
Q.25 The distance travelled (in meters) by the particle from time
t = 0 to t = t will be –
(a)
2
2 2t
sint p-
p
p
(b)
2
2 2t
sint - p+
p
p
(c)
2t
p
(d) None of these
Q.26 The magnitude of displacement (in meters) by the particle
from time t = 0 to t = t will be –
(a)
2
2 2t
sint p-
p
p
(b)
2
2 2t
sint - p+
p
p
(c)
2t
p
(d) None of these
DIRECTIONS (Qs. 27-Q.29) : Each of these questions
contains two statements: Statement-1 (Assertion) and
Statement-2 (Reason). Each of these questions has four
alternative choices, only one of which is the correct answer.
You have to select the correct choice.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a
correct explanation for  Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is
NOT a correct explanation for Statement-1.
(c) Statement -1 is False, Statement-2 is True.
(d) Statement -1 is True, Statement-2 is False.
Q.27 Statement-1 : The position-time graph of a uniform motion
in one dimension of a body can have negative slope.
Statement-2 : When the speed of body decreases with time,
the position-time graph of the moving body has negative slope.
Q.28Statement-1 : A body having non-zero acceleration can
have a constant velocity.
Statement-2 : Acceleration is the rate of change of velocity .
Q.29 Statement-1 : Displacement of a body may be zero when
distance travelled by it is not zero.
Statement-2 : The displacement is the longest distance
between initial and final position.