Question 1: Palette 1/54

DPT MCQ

Ram takes path 1 (straight line) to go from $P$ to $Q$ and Shyam takes path 2 (semicircle) of diameter $100\text{ m}$.
(a) Find the distance travelled by Ram and Shyam.
(b) Find the displacement of Ram and Shyam.

A

(a) Ram $= 100\text{ m}$, Shyam $= 100\text{ m}$; (b) Ram $= 50\pi\text{ m}$, Shyam $= 100\text{ m}$

B

(a) Ram $= 100\text{ m}$, Shyam $= 50\pi\text{ m}$; (b) Ram $= 100\text{ m}$, Shyam $= 100\text{ m}$

C

(a) Ram $= 50\pi\text{ m}$, Shyam $= 100\text{ m}$; (b) Ram $= 100\text{ m}$, Shyam $= 50\pi\text{ m}$

D

(a) Ram $= 100\text{ m}$, Shyam $= 100\pi\text{ m}$; (b) Ram $= 50\text{ m}$, Shyam $= 50\text{ m}$

Question 2: Palette 2/54

DPT MCQ

The position $x$ (in metre) of a particle varies with time $t$ (in second) as $t = \sqrt{x} + 3$. Calculate the:
(a) displacement of the particle from $t = 0$ to $t = 3\text{ s}$
(b) displacement of the particle from $t = 3$ to $t = 6\text{ s}$
(c) distance travelled and displacement from $t = 0$ to $t = 6\text{ s}$

A

(a) $-9\text{ m}$, (b) $+9\text{ m}$, (c) distance $= 18\text{ m}$, displacement $= 0\text{ m}$

B

(a) $+9\text{ m}$, (b) $-9\text{ m}$, (c) distance $= 9\text{ m}$, displacement $= 18\text{ m}$

C

(a) $-9\text{ m}$, (b) $+9\text{ m}$, (c) distance $= 0\text{ m}$, displacement $= 18\text{ m}$

D

(a) $0\text{ m}$, (b) $+9\text{ m}$, (c) distance $= 18\text{ m}$, displacement $= 9\text{ m}$

Question 3: Palette 3/54

DPT MCQ

A particle starts from point $(1, 1, 1)\text{ m}$ and reaches at point $(4, 5, 13)\text{ m}$. Find the initial position vector, final position vector, and displacement vector.

A

Initial: $4\hat{i} + 5\hat{j} + 13\hat{k}$, Final: $\hat{i} + \hat{j} + \hat{k}$, Displacement: $-3\hat{i} - 4\hat{j} - 12\hat{k}$

B

Initial: $\hat{i} + \hat{j} + \hat{k}$, Final: $4\hat{i} + 5\hat{j} + 13\hat{k}$, Displacement: $5\hat{i} + 6\hat{j} + 14\hat{k}$

C

Initial: $\hat{i} + \hat{j} + \hat{k}$, Final: $4\hat{i} + 5\hat{j} + 13\hat{k}$, Displacement: $3\hat{i} + 4\hat{j} + 12\hat{k}$

D

Initial: $3\hat{i} + 4\hat{j} + 12\hat{k}$, Final: $4\hat{i} + 5\hat{j} + 13\hat{k}$, Displacement: $\hat{i} + \hat{j} + \hat{k}$

Question 4: Palette 4/54

DPT MCQ

A body moves $6\text{ m}$ north, $8\text{ m}$ east and $10\text{ m}$ vertically upwards. What is its resultant displacement from initial position?

A

$10\text{ m}$

B

$\frac{10}{\sqrt{2}}\text{ m}$

C

$20\text{ m}$

D

$10\sqrt{2}\text{ m}$

Question 5: Palette 5/54

DPT MCQ

A man goes $10\text{ m}$ towards North, then $20\text{ m}$ towards East. What is his displacement?

A

$25.5\text{ m}$

B

$22.36\text{ m}$

C

$30.0\text{ m}$

D

$25.0\text{ m}$

Question 6: Palette 6/54

DPT MCQ

An aeroplane flies from $P(-4\text{ m}, -5\text{ m}, +8\text{ m})$ to $Q(7\text{ m}, -2\text{ m}, -3\text{ m})$ in an xyz coordinate system. The displacement position vector of the aeroplane is

A

$11\hat{i} + 3\hat{j} + 11\hat{k}$

B

$11\hat{i} - 3\hat{j} + 11\hat{k}$

C

$11\hat{i} + 3\hat{j} - 11\hat{k}$

D

$11\hat{i} - 3\hat{j} - 11\hat{k}$

Question 7: Palette 7/54

DPT MCQ

A body moves in circular path of radius $R$ from $A$ to $B$ as shown. Its displacement and distance covered are

A

$R, \frac{3\pi R}{2}$

B

$\sqrt{2}R, \frac{\pi R}{2}$

C

$\sqrt{2}R, \frac{3\pi R}{2}$

D

None of these

Question 8: Palette 8/54

DPT MCQ

A particle covers half of the circle of radius $r$. Then the displacement and distance of the particle are respectively

A

$2\pi r, 0$

B

$2r, \pi r$

C

$\frac{\pi r}{2}, 2r$

D

$\pi r, r$

Question 9: Palette 9/54

DPT MCQ

A particle moves $5\text{ m}$ along east, $6\text{ m}$ along north, and $10\text{ m}$ in the upward direction. Find its distance and displacement.

A

Distance = $21\text{ m}$, Displacement = $15\text{ m}$

B

Distance = $15\text{ m}$, Displacement = $\sqrt{161}\text{ m}$

C

Distance = $21\text{ m}$, Displacement = $\sqrt{161}\text{ m}$

D

Distance = $21\text{ m}$, Displacement = $21\text{ m}$

Question 10: Palette 10/54

DPT MCQ

A particle moves $10\text{ m}$ east, $5\text{ m}$ north, $6\text{ m}$ south, $8\text{ m}$ west, $15\text{ m}$ east, and $20\text{ m}$ north. Find its total distance and displacement vector.

A

Distance = $64\text{ m}$, Displacement = $17\hat{i} + 19\hat{j}\text{ m}$

B

Distance = $58\text{ m}$, Displacement = $17\hat{i} + 19\hat{j}\text{ m}$

C

Distance = $64\text{ m}$, Displacement = $19\hat{i} + 17\hat{j}\text{ m}$

D

Distance = $60\text{ m}$, Displacement = $10\hat{i} + 20\hat{j}\text{ m}$

Question 11: Palette 11/54

DPT MCQ

A particle travels half of total distance with speed $v_1$ and next half with speed $v_2$ along a straight line. Find out the average speed of the particle.

A

$\frac{2v_1 v_2}{v_1 + v_2}$

B

$\frac{v_1 + v_2}{2}$

C

$\frac{v_1 v_2}{v_1 + v_2}$

D

$\sqrt{v_1 v_2}$

Question 12: Palette 12/54

DPT MCQ

A car travels the first half of a distance between two places at a speed of $30\text{ km/hr}$ and the second half of the distance at $50\text{ km/hr}$. The average speed of the car for the whole journey is

A

$42.5\text{ km/hr}$

B

$40.0\text{ km/hr}$

C

$37.5\text{ km/hr}$

D

$35.0\text{ km/hr}$

Question 13: Palette 13/54

DPT MCQ

A car travels from $A$ to $B$ at a speed of $20\text{ km h}^{-1}$ and returns at a speed of $30\text{ km h}^{-1}$. The average speed of the car for the whole journey is

A

$5\text{ km h}^{-1}$

B

$24\text{ km h}^{-1}$

C

$25\text{ km h}^{-1}$

D

$50\text{ km h}^{-1}$

Question 14: Palette 14/54

DPT MCQ

A car travels from A to B at a speed of $20\text{ km/hr}$ and returns at a speed of $30\text{ km/hr}$. The average speed of the car for the whole journey is

A

$25\text{ km/hr}$

B

$24\text{ km/hr}$

C

$50\text{ km/hr}$

D

$5\text{ km/hr}$

Question 15: Palette 15/54

DPT MCQ

A boy walks to his school at a distance of $6\text{ km}$ with constant speed of $2.5\text{ km/hr}$ and walks back with a constant speed of $4\text{ km/hr}$. His average speed for round trip expressed in $\text{km/hour}$, is

A

$\frac{24}{13}$

B

$\frac{40}{13}$

C

$3$

D

$\frac{1}{2}$

Question 16: Palette 16/54

DPT MCQ

A car travels the first half of a distance between two places at a speed of $30\text{ km/hr}$ and the second half of the distance at $50\text{ km/hr}$. The average speed of the car for the whole journey is

A

$42.5\text{ km/hr}$

B

$40.0\text{ km/hr}$

C

$37.5\text{ km/hr}$

D

$35.0\text{ km/hr}$

Question 17: Palette 17/54

DPT MCQ

A man walks on a straight road from his home to a market $2.5\text{ km}$ away with a speed of $5\text{ km/h}$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5\text{ km/h}$. The average speed of the man over the interval of time $0$ to $40\text{ min}$ is equal to

A

$5\text{ km/h}$

B

$\frac{25}{4}\text{ km/h}$

C

$\frac{30}{4}\text{ km/h}$

D

$\frac{45}{8}\text{ km/h}$

Question 18: Palette 18/54

DPT MCQ

One car moving on a straight road covers one third of the distance with $20\text{ km/hr}$ and the rest with $60\text{ km/hr}$. The average speed is

A

$40\text{ km/hr}$

B

$80\text{ km/hr}$

C

$46\frac{2}{3}\text{ km/hr}$

D

$36\text{ km/hr}$

Question 19: Palette 19/54

DPT MCQ

If a car covers $\frac{2}{5}\text{th}$ of the total distance with $v_1$ speed and $\frac{3}{5}\text{th}$ distance with $v_2$, then average speed is

A

$\frac{1}{2}\sqrt{v_1 v_2}$

B

$\frac{v_1 + v_2}{2}$

C

$\frac{2v_1 v_2}{v_1 + v_2}$

D

$\frac{5v_1 v_2}{3v_1 + 2v_2}$

Question 20: Palette 20/54

DPT MCQ

A person travelling on a straight line moves with a uniform velocity $v_1$ for some time and with uniform velocity $v_2$ for the next equal time. The average velocity $v$ is given by

A

$v = \frac{v_1 + v_2}{2}$

B

$v = \sqrt{v_1 v_2}$

C

$v = \frac{2v_1 v_2}{v_1 + v_2}$

D

$v = \frac{v_1 v_2}{v_1 + v_2}$

Question 21: Palette 21/54

DPT MCQ

A man walks for some time $t$ with velocity $v$ due east. Then he walks for same time $t$ with velocity $v$ due north. The average speed of the man is

A

$2v$

B

$\sqrt{2}v$

C

$v$

D

$\frac{v}{\sqrt{2}}$

Question 22: Palette 22/54

DPT MCQ

A car travels a distance $d$ on a straight road in two hours and then returns to the starting point in next three hours. Its average speed and average velocity is

A

$\frac{d}{5}, 0$

B

$\frac{2d}{5}, 0$

C

$\frac{5d}{6}, \frac{d}{5}$

D

none of these

Question 23: Palette 23/54

DPT MCQ

A particle moves in the east direction with $15\text{ m/s}$ for $2\text{ s}$ then northwards with $5\text{ m/s}$ for $8\text{ s}$. Average velocity of the particle is

A

$1\text{ m/s}$

B

$5\text{ m/s}$

C

$7\text{ m/s}$

D

$10\text{ m/s}$

Question 24: Palette 24/54

DPT MCQ

An object travels $10\text{ km}$ at a speed of $100\text{ m/s}$ and another $10\text{ km}$ at $50\text{ m/s}$. The average speed over the whole distance is

A

$75\text{ m/s}$

B

$55\text{ m/s}$

C

$66.7\text{ m/s}$

D

$33.3\text{ m/s}$

Question 25: Palette 25/54

DPT MCQ

A particle moves in straight line in same direction for $20\text{ sec.}$ with velocity $3\text{ m/s}$ and then moves with velocity $4\text{ m/s}$ for another $20\text{ sec.}$ and finally moves with velocity $5\text{ m/s}$ for next $20\text{ sec.}$. What is the average velocity of the particle?

A

$3\text{ m/s}$

B

$4\text{ m/s}$

C

$5\text{ m/s}$

D

$\text{Zero}$

Question 26: Palette 26/54

DPT MCQ

A body has speed $V$, $2V$ and $3V$ in first $1/3$ part of total travelled distance $S$, second $1/3$ part of $S$ and third $1/3$ part of $S$ respectively. Its average speed will be

A

$V$

B

$2V$

C

$\frac{18}{11}V$

D

$\frac{11}{18}V$

Question 27: Palette 27/54

DPT MCQ

A body covers one-third of the time with a velocity $v_1$, the second one-third of the time with a velocity $v_2$, and the last one-third of the time with a velocity $v_3$. The average velocity is

A

$\frac{v_1 + v_2 + v_3}{3}$

B

$\frac{3v_1 v_2 v_3}{v_1 v_2 + v_2 v_3 + v_3 v_1}$

C

$\frac{v_1 v_2 + v_2 v_3 + v_3 v_1}{3}$

D

$\frac{v_1 v_2 v_3}{3}$

Question 28: Palette 28/54

DPT MCQ

A particle moving in a straight line covers half the distance with speed of $10\text{ m/s}$. The other half of the distance is covered in two equal time intervals with speed of $4.5\text{ m/s}$ and $7.5\text{ m/s}$ respectively. The average speed of the particle during this motion is

A

$8.0\text{ m/s}$

B

$12.0\text{ m/s}$

C

$10.0\text{ m/s}$

D

$7.5\text{ m/s}$

Question 29: Palette 29/54

DPT MCQ

A point object traverses half the distance with velocity $v_0$. The remaining part of the distance is covered with velocity $v_1$ for half the time and with velocity $v_2$ for the rest half. The average velocity of the object for the whole journey is

A

$\frac{2v_1 (v_0 + v_2)}{v_0 + 2v_1 + 2v_2}$

B

$\frac{2v (v_0 + v_1)}{v_0 + v_1 + v_2}$

C

$\frac{2v_0 (v_1 + v_2)}{v_1 + v_2 + 2v_0}$

D

$\frac{2v_2 (v_0 + v_1)}{v_1 + 2v_2 + v_0}$

Question 30: Palette 30/54

DPT MCQ

If a train travels $\frac{1}{4}\text{th}$ of the total distance with speed $v_1$ and the remaining $\frac{3}{4}\text{th}$ distance with speed $v_2$, then its average speed is

A

$\frac{4v_1 v_2}{3v_1 + v_2}$

B

$\frac{v_1 + 3v_2}{4}$

C

$\frac{3v_1 v_2}{v_1 + 3v_2}$

D

$\frac{v_1 v_2}{v_1 + v_2}$

Question 31: Palette 31/54

DPT MCQ

The motion of a particle is described by the equation $x = a + bt^2$ where $a = 15 \text{ cm}$ and $b = 3 \text{ cm/s}^2$. Its instantaneous velocity at time $3 \text{ sec}$ will be

A

36 cm/sec

B

18 cm/sec

C

16 cm/sec

D

32 cm/sec

Question 32: Palette 32/54

DPT MCQ

A train has a speed of 60 km/h for the first one hour and 40 km/h for the next half hour. Its average speed in km/h is

A

50

B

53.33

C

48

D

70

Question 33: Palette 33/54

DPT MCQ

A person completes half of his journey with speed $v_1$ and rest half with speed $v_2$. The average speed of the person is

A

$v = \frac{v_1 + v_2}{2}$

B

$v = \frac{2v_1 v_2}{v_1 + v_2}$

C

$v = \frac{v_1 v_2}{v_1 + v_2}$

D

$v = \sqrt{v_1 v_2}$

Question 34: Palette 34/54

DPT MCQ

A car moving on a straight road covers one third of the distance with 20 km/hr and the rest with 60 km/hr. The average speed is

A

40 km/hr

B

80 km/hr

C

$46\frac{2}{3} \text{ km/hr}$

D

36 km/hr

Question 35: Palette 35/54

DPT MCQ

The displacement of a particle, moving in a straight line, is given by $s = 2t^2 + 2t + 4$ where $s$ is in metres and $t$ in seconds. The acceleration of the particle is

A

$2 \text{ m/s}^2$

B

$4 \text{ m/s}^2$

C

$6 \text{ m/s}^2$

D

$8 \text{ m/s}^2$

Question 36: Palette 36/54

DPT MCQ

The position $x$ of a particle varies with time $t$ as $x = at^2 - bt^3$. The acceleration of the particle will be zero at time $t$ equal to

A

$\frac{a}{b}$

B

$\frac{2a}{3b}$

C

$\frac{a}{3b}$

D

Zero

Question 37: Palette 37/54

DPT MCQ

The displacement of the particle is given by $y = a + bt + ct^2 - dt^4$. The initial velocity and acceleration are respectively

A

$b, -4d$

B

$-b, 2c$

C

$b, 2c$

D

$2c, -4d$

Question 38: Palette 38/54

DPT MCQ

The relation between time $t$ and distance $x$ is $t = \alpha x^2 + \beta x$, where $\alpha$ and $\beta$ are constants. The retardation is ($v$ is the velocity)

A

$2\alpha v^3$

B

$2\beta v^3$

C

$2\alpha\beta v^3$

D

$2\beta^2 v^3$

Question 39: Palette 39/54

DPT MCQ

If displacement of a particle is directly proportional to the square of time, then the particle is moving with

A

Variable acceleration

B

Uniform acceleration

C

Uniform velocity

D

Variable acceleration but uniform velocity

Question 40: Palette 40/54

DPT MCQ

A particle is moving eastwards with velocity of $5 \text{ m/s}$. In $10 \text{ sec}$ the velocity changes to $5 \text{ m/s}$ northwards. The average acceleration in this time is

A

Zero

B

$\frac{1}{\sqrt{2}} \text{ m/s}^2$ toward north-west

C

$\frac{1}{\sqrt{2}} \text{ m/s}^2$ toward north-east

D

$\frac{1}{2} \text{ m/s}^2$ toward north-west

Question 41: Palette 41/54

DPT MCQ

A body of mass 10 kg is moving with a constant velocity of $10 \text{ m/s}$. When a constant force acts for $4 \text{ sec}$ on it, it moves with a velocity $2 \text{ m/sec}$ in the opposite direction. The acceleration produced in it is

A

$3 \text{ m/s}^2$

B

$-3 \text{ m/s}^2$

C

$0.3 \text{ m/s}^2$

D

$-0.3 \text{ m/s}^2$

Question 42: Palette 42/54

DPT MCQ

A body starts from the origin and moves along the x-axis such that velocity at any instant is given by $(4t^3 - 2t)$, where $t$ is in second and velocity is in m/s. What is the acceleration of the particle, when it is $2 \text{ m}$ from the origin?

A

$28 \text{ m/s}^2$

B

$22 \text{ m/s}^2$

C

$12 \text{ m/s}^2$

D

$10 \text{ m/s}^2$

Question 43: Palette 43/54

DPT MCQ

The velocity of any particle is related with its displacement as $x = \sqrt{v+1}$. Calculate the acceleration of the particle at $x = 5\text{ m}$.

A

$200\text{ m/s}^2$

B

$240\text{ m/s}^2$

C

$120\text{ m/s}^2$

D

$180\text{ m/s}^2$

Question 44: Palette 44/54

DPT MCQ

The velocity of a particle moving in the positive direction of x-axis varies as $v = \alpha \sqrt{x}$ where $\alpha$ is a positive constant. Assuming that at $t = 0$, the particle was located at $x = 0$, find the acceleration of the particle as a function of time.

A

$\frac{1}{4} \alpha^2 t$

B

$\frac{1}{2} \alpha^2$

C

$\alpha^2 t$

D

$2 \alpha^2$

Question 45: Palette 45/54

DPT MCQ

A 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

$\frac{2v}{a}$

B

$\frac{v}{a}$

C

$\frac{v}{2a}$

D

$\sqrt{\frac{v}{2a}}$

Question 46: Palette 46/54

DPT MCQ

A student is standing at a distance of $50\text{ metres}$ from the bus. As soon as the bus starts its motion with an acceleration of $1\text{ ms}^{-2}$, the student starts running towards the bus with a uniform velocity $u$. Assuming the motion to be along a straight road, the minimum value of $u$, so that the student is able to catch the bus is

A

$8\text{ ms}^{-1}$

B

$12\text{ ms}^{-1}$

C

$10\text{ ms}^{-1}$

D

$5\text{ ms}^{-1}$

Question 47: Palette 47/54

DPT MCQ

A car, moving with a speed of $50\text{ km/hr}$, can be stopped by brakes after at least $6\text{ m}$. If the same car is moving at a speed of $100\text{ km/hr}$, the minimum stopping distance is

A

$6\text{ m}$

B

$12\text{ m}$

C

$18\text{ m}$

D

$24\text{ m}$

Question 48: Palette 48/54

DPT MCQ

The velocity of a bullet is reduced from $200\text{ m/s}$ to $100\text{ m/s}$ while travelling through a wooden block of thickness $10\text{ cm}$. The retardation, assuming it to be uniform, will be

A

$10 \times 10^4\text{ m/s}^2$

B

$12 \times 10^4\text{ m/s}^2$

C

$13.5 \times 10^4\text{ m/s}^2$

D

$15 \times 10^4\text{ m/s}^2$

Question 49: Palette 49/54

DPT MCQ

A body A starts from rest with an acceleration $a_1$. After $2\text{ seconds}$, another body B starts from rest with an acceleration $a_2$. If they travel equal distances in the $5\text{th}$ second, after the start of A, then the ratio $a_1 : a_2$ is equal to

A

$5:9$

B

$5:7$

C

$9:5$

D

$9:7$

Question 50: Palette 50/54

DPT MCQ

The average velocity of a body moving with uniform acceleration travelling a distance of $3.06\text{ m}$ is $0.34\text{ ms}^{-1}$. If the change in velocity of the body is $0.18\text{ ms}^{-1}$ during this time, its uniform acceleration is

A

$0.01\text{ ms}^{-2}$

B

$0.02\text{ ms}^{-2}$

C

$0.03\text{ ms}^{-2}$

D

$0.04\text{ ms}^{-2}$

Question 51: Palette 51/54

DPT MCQ

A particle travels $10\text{ m}$ in first $5\text{ sec}$ and $10\text{ m}$ in next $3\text{ sec}$. Assuming constant acceleration what is the distance travelled in next $2\text{ sec}$

A

$8.3\text{ m}$

B

$9.3\text{ m}$

C

$10.3\text{ m}$

D

None of above

Question 52: Palette 52/54

DPT MCQ

A body travels for $15\text{ sec}$ 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

$S_1 = \frac{1}{3}S_2 = \frac{1}{5}S_3$

D

$S_1 = \frac{1}{5}S_2 = \frac{1}{3}S_3$

Question 53: Palette 53/54

DPT MCQ

If a body having initial velocity zero is moving with uniform acceleration $8\text{ m/sec}^2$, the distance travelled by it in fifth second will be

A

$36\text{ metres}$

B

$40\text{ metres}$

C

$100\text{ metres}$

D

Zero

Question 54: Palette 54/54

DPT MCQ

The engine of a car produces acceleration $4\text{ m/s}^2$ in the car, if this car pulls another car of same mass, what will be the acceleration produced

A

$8\text{ m/s}^2$

B

$2\text{ m/s}^2$

C

$4\text{ m/s}^2$

D

$\frac{1}{2}\text{ m/s}^2$