Question 1: Palette 1/56

Error less MCQ

A man goes 10 m towards North, then 20 m towards East. What is his displacement?

A

22.5 m

B

25 m

C

25.5 m

D

30 m

Question 2: Palette 2/56

Error less MCQ

A body moves over one fourth of a circular arc in a circle of radius $r$. The magnitude of distance travelled and displacement will be respectively

A

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

B

$\frac{\pi r}{4}, r$

C

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

D

$\pi r, r$

Question 3: Palette 3/56

Error less MCQ

The displacement of the point of the wheel initially in contact with the ground, when the wheel rolls forward half a revolution will be (radius of the wheel is $R$)

A

$\frac{R}{\sqrt{\pi^2 + 4}}$

B

$R\sqrt{\pi^2 + 4}$

C

$2\pi R$

D

$\pi R$

Question 4: Palette 4/56

Error less 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 5: Palette 5/56

Error less MCQ

A car accelerated from initial position and then returned at initial point, then

A

Velocity is zero but speed increases

B

Speed is zero but velocity increases

C

Both speed and velocity increase

D

Both speed and velocity decrease

Question 6: Palette 6/56

Error less MCQ

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

A

5 km/h

B

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

C

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

D

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

Question 7: Palette 7/56

Error less MCQ

The position of a particle moving along the x-axis at certain times is given below:
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 generalisation

Question 8: Palette 8/56

Error less MCQ

Which of the following graphs represents uniform motion?

A

B

C

D

Question 9: Palette 9/56

Error less MCQ

The displacement-time graph for two particles $A$ and $B$ are straight lines inclined at angles of $30^\circ$ and $60^\circ$ with the time axis. The ratio of velocities of $v_A : v_B$ is

A

$1 : 2$

B

$1 : \sqrt{3}$

C

$\sqrt{3} : 1$

D

$1 : 3$

Question 10: Palette 10/56

Error less MCQ

From the following displacement-time graph, find out the velocity of a moving body:
(A graph is given with time on the vertical axis and displacement on the horizontal axis, showing a straight line making an angle of $30^\circ$ with the displacement axis).

A

$\frac{1}{\sqrt{3}} \text{ m/s}$

B

$3 \text{ m/s}$

C

$\sqrt{3} \text{ m/s}$

D

$\frac{1}{3} \text{ m/s}$

Question 11: Palette 11/56

Error less MCQ

The diagram shows the displacement-time graph for a particle moving in a straight line. The average velocity for the interval $t = 0$ to $t = 5$ is

A

$0 \text{ ms}^{-1}$

B

$6 \text{ ms}^{-1}$

C

$-2 \text{ ms}^{-1}$

D

$2 \text{ ms}^{-1}$

Question 12: Palette 12/56

Error less MCQ

Figure shows the displacement-time graph of a body. What is the ratio of the speed in the first second and that in the next two seconds?

A

$1 : 2$

B

$1 : 3$

C

$3 : 1$

D

$2 : 1$

Question 13: Palette 13/56

Error less MCQ

A ball is thrown vertically upwards. Which of the following plots represents the speed-time graph of the ball during its flight if the air resistance is not ignored?

A

B

C

D

Question 14: Palette 14/56

Error less MCQ

A train moves from one station to another in 2 hours time. Its speed-time graph during this motion is shown in the figure. The maximum acceleration during the journey is

A

$100 \text{ km h}^{-2}$

B

$160 \text{ km h}^{-2}$

C

$140 \text{ km h}^{-2}$

D

$120 \text{ km h}^{-2}$

Question 15: Palette 15/56

Error less MCQ

The graph of displacement $v/s$ time shows a downward-opening parabolic curve starting from the origin. Its corresponding velocity-time graph will be:

A

B

C

D

Question 16: Palette 16/56

Error less MCQ

A particle moves along a straight line such that its displacement at any time $t$ is given by $S = t^3 - 6t^2 + 3t + 4$ metres. The velocity when the acceleration is zero is

A

$3 \text{ ms}^{-1}$

B

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

C

$42 \text{ ms}^{-1}$

D

$-9 \text{ ms}^{-1}$

Question 17: Palette 17/56

Error less MCQ

A body is moving according to the equation $x = at + bt^2 - ct^3$ where $x =$ displacement and $a, b$ and $c$ are constants. The acceleration of the body is

A

$2b - 6ct$

B

$a + 2bt$

C

$2b + 6ct$

D

$3b - 6ct^2$

Question 18: Palette 18/56

Error less MCQ

The displacement is given by $x = 2t^2 + t + 5$, the acceleration at $t = 2\text{ s}$ is

A

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

B

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

C

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

D

$15\text{ m/s}^2$

Question 19: Palette 19/56

Error less MCQ

The velocity of a body depends on time according to the equation $v = 20 + 0.1t^2$. The body is undergoing

A

Uniform acceleration

B

Uniform retardation

C

Non-uniform acceleration

D

Zero acceleration

Question 20: Palette 20/56

Error less MCQ

The displacement of a body is given to be proportional to the cube of time elapsed. The magnitude of the acceleration of the body is

A

Increasing with time

B

Decreasing with time

C

Constant but not zero

D

Zero

Question 21: Palette 21/56

Error less MCQ

The correct statement from the following is

A

A body having zero velocity will not necessarily have zero acceleration

B

A body having zero velocity will necessarily have zero acceleration

C

A body having uniform speed can have only uniform acceleration

D

A body having non-uniform velocity will have zero acceleration

Question 22: Palette 22/56

Error less MCQ

A particle moves along a straight line such that its displacement at any time $t$ is given by $s = t^3 - 3t^2 + 2\text{ meter}$. The displacement when the acceleration becomes zero is

A

$0\text{ meter}$

B

$2\text{ meter}$

C

$3\text{ meter}$

D

$-2\text{ meter}$

Question 23: Palette 23/56

Error less MCQ

What is the angle between instantaneous displacement and acceleration during the retarded motion

A

Zero

B

$\frac{\pi}{4}$

C

$\frac{\pi}{2}$

D

$\pi$

Question 24: Palette 24/56

Error less MCQ

The acceleration of a particle starting from rest, varies with time according to the relation $A = -a\omega^2 \sin\omega t$. The displacement of this particle at a time $t$ will be

A

$-\frac{1}{2}(a\omega^2 \sin\omega t)t^2$

B

$a\omega \sin\omega t$

C

$a\omega \cos\omega t$

D

$a \sin\omega t$

Question 25: Palette 25/56

Error less MCQ

If the velocity of a particle is $(10 + 2t^2) \text{ m/s}$, then the average acceleration of the particle between $2\text{ s}$ and $5\text{ s}$ is

A

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

B

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

C

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

D

$14 \text{ m/s}^2$

Question 26: Palette 26/56

Error less MCQ

The displacement versus time graph for a body moving in a straight line is shown from the image given below. Which of the following regions represents the motion when no force is acting on the body?

A

$ab$

B

$bc$

C

$cd$

D

$de$

Question 27: Palette 27/56

Error less MCQ

A car decelerates at a constant rate during a period commencing at $t = 0$. Which of the displacement time graphs represents the displacement of the car from the image given below?

A

(a)

B

(b)

C

(c)

D

(d)

Question 28: Palette 28/56

Error less MCQ

Which of the following can not be the distance time graph from the image given below?

A

(a)

B

(b)

C

(c)

D

(d)

Question 29: Palette 29/56

Error less MCQ

Which of the following displacement time graphs is not possible from the image given below?

A

Graph (a)

B

Graph (b)

C

Graph (c)

D

Graph (d)

Question 30: Palette 30/56

Error less MCQ

The graph between the displacement $x$ and time $t$ for a particle moving in a straight line is shown from the image gven below. During the intervals $OA$, $AB$, $BC$, and $CD$, what is the sign of the acceleration of the particle?

A

$+$, $0$, $+$, $x$

B

$-$, $0$, $+$, $0$

C

$+$, $0$, $-$, $x$

D

$-$, $0$, $-$, $0$

Question 31: Palette 31/56

Error less MCQ

The $x-t$ graph represents from the image gven below

A

Constant velocity

B

Velocity of the body continuously changing

C

Instantaneous velocity

D

The body travels with constant speed upto time $t_1$ and then stops

Question 32: Palette 32/56

Error less MCQ

An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement $s$ -velocity $v$ graph of this object is from the image given below

A

A parabola opening towards the $s$-axis

B

A curve curving towards the $v$-axis

C

A parabola opening upwards along $s$-axis starting after a constant offset

D

A straight line passing through origin

Question 33: Palette 33/56

Error less MCQ

The variation of velocity of a particle with time moving along a straight line is illustrated in the graph from the image given below. The distance travelled by the particle in four seconds is

A

60 m

B

55 m

C

25 m

D

30 m

Question 34: Palette 34/56

Error less MCQ

A car accelerates from rest at a constant rate $\alpha$ for some time, after which it decelerates at a constant rate $\beta$ and comes to rest. If the total time elapsed in $t$, then the maximum velocity acquired by the car is

A

$(\frac{\alpha^{2}+\beta^{2}}{\alpha\beta})t$

B

$(\frac{\alpha^{2}-\beta^{2}}{\alpha\beta})t$

C

$\frac{(\alpha+\beta)t}{\alpha\beta}$

D

$\frac{\alpha\beta t}{\alpha+\beta}$

Question 35: Palette 35/56

Error less MCQ

A rocket is projected vertically upwards, whose velocity-time graph is shown in fig. The maximum height reached by the rocket is from the image given below

A

1 km

B

10 km

C

20 km

D

60 km

Question 36: Palette 36/56

Error less MCQ

In the above problem the mean velocity of rocket in reaching the maximum height will be from the image given below A rocket is projected vertically upwards, whose velocity-time graph is shown in fig.

A

100 m/s

B

50 m/s

C

500 m/s

D

25/3 m/s

Question 37: Palette 37/56

Error less MCQ

In the above problem the acceleration of rocket will be from the image given below A rocket is projected vertically upwards, whose velocity-time graph is shown in fig.

A

$50 \text{ m/s}^2$

B

$100 \text{ m/s}^2$

C

$500 \text{ m/s}^2$

D

$250 \text{ m/s}^2$

Question 38: Palette 38/56

Error less MCQ

A lift is going up. The variation in the speed of the lift is as given in the graph. What is height to which the lift takes the passenger from the image given below

A

3.6 m

B

28.8 m

C

36.0 m

D

Cannot be calculated from the above graph

Question 39: Palette 39/56

Error less MCQ

The figure shows the velocity of a particle plotted against time $t$ from the image given below

A

The displacement of the particle is zero

B

The particle changes its direction of motion at some point

C

The initial and final speeds of the particle are same

D

All of the above statements are correct

Question 40: Palette 40/56

Error less MCQ

The $v-t$ plot of a moving object is shown in the figure from the image given below. The average velocity of the object during the first 10 seconds is

A

0

B

$2.5 \text{ ms}^{-1}$

C

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

D

$2 \text{ ms}^{-1}$

Question 41: Palette 41/56

Error less MCQ

Which of the following velocity time graphs is possible from the image given below

A

B

C

D

Question 42: Palette 42/56

Error less MCQ

A particle starts from rest, accelerates at $2 \text{ m/s}^2$ for $10\text{ s}$ and then goes for constant speed for $30\text{ s}$ and then decelerates at $4 \text{ m/s}^2$ till it stops. What is the distance travelled by it

A

750 m

B

800 m

C

700 m

D

850 m

Question 43: Palette 43/56

Error less MCQ

The graph below shows the velocity versus time graph for a body from the image given below. Which of the following graphs represents the corresponding acceleration versus time graphs

A

B

C

D

Question 44: Palette 44/56

Error less MCQ

The acceleration-time graph for a body is shown in the following graph from the image given below. Which of the following graphs would probably represent the velocity of the body plotted against time

A

B

C

D

Question 45: Palette 45/56

Error less MCQ

A particle is moving in such a way that its displacement is related with time by the equation $x = (10 - 4t + 6t^2) \text{ m}$. The diagram showing variation of velocity of particle with time is from the image given below

A

B

C

D

Question 46: Palette 46/56

Error less MCQ

In the velocity-time graph from the image given below, the distance travelled by the body in metres is

A

200

B

250

C

300

D

400

Question 47: Palette 47/56

Error less MCQ

For the velocity-time graph shown from the image given below, the distance covered by the body in the last two seconds of its motion is what fraction of the total distance covered by it in all the seven seconds?

A

1/2

B

1/4

C

1/3

D

2/3

Question 48: Palette 48/56

Error less MCQ

The velocity-time graph of a body moving in a straight line is shown from the image gven below. The displacement and distance travelled by the body in 6 s are respectively

A

8 m, 16 m

B

16 m, 8 m

C

16 m, 16 m

D

8 m, 8 m

Question 49: Palette 49/56

Error less MCQ

A ball is thrown vertically upward. Which of the following graphs from the image given below represents the velocity-time graph of the ball during its flight when air resistance is neglected?

A

B

C

D

Question 50: Palette 50/56

Error less MCQ

A ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $d/2$. Neglecting subsequent motion and air resistance, its velocity $v$ varies with the height $h$ above the ground as shown from the image given below:

A

B

C

D

Question 51: Palette 51/56

Error less MCQ

The acceleration-time graph of a body is shown from the image given below. The most probable velocity-time graph of the body is

A

B

C

D

Question 52: Palette 52/56

Error less MCQ

Which of the following velocity-time graphs is not possible from the image given below?

A

B

C

D

Question 53: Palette 53/56

Error less MCQ

For a certain body, the velocity-time graph is shown from the image given below. The ratio of applied forces for intervals AB and BC is

A

$+ \frac{1}{\sqrt{3}}$

B

$- \frac{1}{\sqrt{3}}$

C

$+ \sqrt{3}$

D

$- \frac{1}{3}$

Question 54: Palette 54/56

Error less MCQ

Velocity-time graphs of two cars which start from rest at the same time, are shown from the image given below. Graph shows, that

A

Initial velocity of A is greater than the initial velocity of B

B

Acceleration in A is increasing at lesser rate than in B

C

Acceleration in A is greater than in B

D

Acceleration in B is greater than in A

Question 55: Palette 55/56

Error less MCQ

Which one of the following graphs represents the velocity of a steel ball which falls from a height on to a marble floor from the image given below? (Here $v$ represents the velocity of the particle and $t$ the time)

A

B

C

D

Question 56: Palette 56/56

Error less MCQ

The adjoining curve represents the velocity-time graph of a particle, its acceleration values along OA, AB and BC in $m/s^2$ from the image given below are respectively

A

1, 0, -0.5

B

1, 0, 0.5

C

1, 1, 0.5

D

1, 0.5, 0