Motion PYQs - Last 10 Years

Two spheres are projected at angles $30^\circ$ and $45^\circ$ with the horizontal. The maximum height reached by both is same. The ratio of their initial velocities is, $\left(\sin 45^\circ = \dfrac{1}{\sqrt{2}}, \sin 30^\circ = 0.5\right)$

The equation of the trajectory of a ball projected at an angle $\theta$ with the horizontal, is given as $y = x - \dfrac{gx^2}{2}$The initial velocity of the ball is[Given : $\tan 45^\circ = 1$, $\cos 45^\circ = \dfrac{1}{\sqrt{2}}$ ]

For a projectile motion, the range R is 'n' times the maximum height H. So the angle of projection is

Two balls A and B are projected at an angle of $45^\circ$ and $60^\circ$ respectively, so that the maximum heights reached are same for both. The ratio of initial velocity of projection of ball A to that for ball B is$(\sin 30^\circ = \cos ...

A ball P is projected at an angle of $60^\circ$ with the vertical with certain initial speed. Another ball Q of the same mass as that of ball P is projected vertically upwards with the same initial speed as that of P. At the highest point, ...

Two boys are standing at points A and B on ground where distance AB = a. The boy at point B starts running perpendicular to line AB with velocity '$V_1$'. The boy at point A starts running simultaneously with velocity 'V' and catches the ot...

A ball is released from height 'h' which makes perfectly elastic collision with ground. The frequency of periodic vibratory motion is (g=acceleration due to gravity)

Two objects are projected with same velocity 'u' at different angles $\alpha$ and $\beta$ with the horizontal. If $\alpha + \beta = 90^\circ$, the ratio of horizontal range of the first object to the second object will be $[\sin(\pi - \thet...

A stone falls from the top of a tower of height $100$ m and at the same time another stone is projected vertically upwards from the ground with a velocity $25$ m/s. The two stones meet after

A batsman hits a ball with a velocity 'v', making an angle of $60^\circ$ with the vertical. After some time direction of velocity is making an angle of $60^\circ$ with the horizontal. The speed of the ball at this instant is$\left[\cos(60^\...

The velocity time graph of a body moving in a straight line is shown in a figure. The ratio of displacement to distance travelled by the body in time $0$ to $10$ s is

A car passes three points A, B and C at $3$ m/s, $6$ m/s and $9$ m/s respectively in a straight line with uniform acceleration. If distance $AB = 60$ m then find the distance BC.

A boy throws a ball vertically upwards from a bridge with velocity $5 \mathrm{~m} / \mathrm{s}$. It strikes water surface after 2 s . The height of the bridge is (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

A car moving at a speed ' V ' is stopped in a certain distance when the breaks produce a deceleration ' $a$ '. If the speed of the car is ' $n v$ ', what must be the deceleration of the car to stop it in the same distance and in the same ti...

Two boys are standing at points A and B on ground, where distance $\mathrm{AB}=\mathrm{x}$. The boy at B stars running perpendicular to $A B$ with velocity $\mathrm{v}_1$. The boy at A starts running simultaneously with velocity v and meets...

Two girls are standing at the ends ' $A$ ' and ' $B$ ' of a ground where $\mathrm{AB}=\mathrm{b}$. The girl at ' B ' starts running in a direction perpendicular to ' $A B$ ' with velocity ' $\mathrm{V}_1$ '. The girl at ' A ' starts running...

The acceleration (a) - time (T) graph for the body starting from rest is given below. The maximum speed of the body is

A body when projected at an angle ' $\theta$ ' with the horizontal reaches a maximum height ' $H$ '. The time of flight of the body will be ( $\mathrm{g}=$ acceleration due to gravity)

At any time ' $t$ ', the co-ordinates of moving particle are $x=a t^2$ and $y=b t^2$. The speed of the particle is

The velocity time graph of a body moving in a straight line is shown in figure. The ratio of displacement to distance travelled by the body in time 0 to 8 s is

A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered by the body in the $n^{\text {th }}$ second of its motion to the total distance travelled in n second is

Two bodies A and B move in same straight line starting from same position. Body moves with constant velocity ' u ' and body B moves with constant acceleration ' $a$ '. When their velocities become equal, the distance between them is

A force acting on a body of mass 5 Kg is $(4 \hat{i}-2 \hat{j}+3 \hat{k}) \mathrm{N}$. If the body is initially at rest then the magnitude of its velocity at the end of 10 second in $\mathrm{m} / \mathrm{s}$ will be

A velocity - time graph of a body is shown below. The distance covered by the body from 6 second to 9 second is

The following figures show the variation of displacement with time of a particular object.

Which of the following person is in an inertial frame of reference?

For a projectile, the maximum height and horizontal range are same. The angle of projection ' $\theta$ ' of the projectile is

The ratio of weight of a man in a stationery lift and weight when the lift is moving downward with a uniform acceleration ' $a$ ' is $3: 2$. Then the value of ' $a$ ' is

The acceleration of a moving body can be found from

A driver applies the brakes on seeing the red traffic signal 400 m ahead. At the time of applying brakes, the vehicle was moving with $15 \mathrm{~m} / \mathrm{s}$ and retarding at $0.3 \mathrm{~m} / \mathrm{s}^2$. The distance covered by t...

The co-ordinates of a moving particle at any time ' $t$ ' are given by $x=\alpha t^3$ and $y=\beta t^3$ where $\alpha$ and $\beta$ are constants. The speed of the particle at time ' $t$ ' is given by

A body travelling with uniform acceleration crosses two points A and B with velocities $20 \mathrm{~m} / \mathrm{s}$ and $30 \mathrm{~m} / \mathrm{s}$ respectively. The speed of the body at mid point of A and B is (nearly)

A ball is released from the top of a tower of height Hm . It takes T second to reach the ground. The height of the ball from the ground after $\frac{T}{4}$ second is

For the velocity-time graph shown in the figure below, the distance covered by the body in last two second of its motion is ' $\mathrm{S}_1$ '. What is the ratio of ' $\mathrm{S}_1$ ' to the total distance covered by it

A bullet is fired on a target with velocity V . Its velocity decreases from V to $\mathrm{V} / 2$. When it penetrates 30 cm in a target. Through what thickness it will penetrate further in the target before coming to rest?

Two cars start from a point at the same time in a straight line and their positions are represented by $x_1(t)=a t+b t^2$ and $x_2(t)=F t-t^2$. At what time do the cars have the same velocity?

A vehicle runs on a straight road of length 'L'. It travels half the distance with speed V and the remaining distance with speed $\frac{\mathrm{V}}{3}$. Its average speed is

The position '\(x\)' of a particle varies with a time as \(x=a t^2-b t^3\) where '\(a\)' and '\(b\)' are constants. The acceleration of the particle will be zero at

Which one of the following statements is Wrong?

A large number of bullets are fired in all directions with same speed '\(U\)'. The maximum area on the ground on which the bullets will spread is

A small steel ball is dropped from a height of \(1.5 \mathrm{~m}\) into a glycerine jar. The ball reaches the bottom of the jar \(1.5 \mathrm{~s}\) after it was dropped. If the retardation is \(2.66 \mathrm{~m} / \mathrm{s}^2\), the height ...

Two bodies \(A\) and \(B\) start from the same point at the same instant and move along a straight line. body \(A\) moves with uniform acceleration \(a\) and body \(B\) moves with uniform velocity \(v\). They meet after time \(t\). The valu...

A ball is projected vertically upwards from ground. It reaches a height '\(h\)' in time \(t_1\), continues its motion and then takes a time \(t_2\) to reach ground. The height $h$ in terms of \(g, t_1\) and \(\mathrm{t}_2\) is $$(\mathrm{g}...

A bullet is fired on a target with velocity '\(\mathrm{V}\)'. Its velocity decreases from '\(\mathrm{V}\)' to '\(\mathrm{V} / 2\)' when it penetrates \(30 \mathrm{~cm}\) in a target. Through what thickness it will penetrate further in the t...

Two cars A and B start from a point at the same time in a straight line and their positions are represented by \(\mathrm{R}_{\mathrm{A}}(\mathrm{t})=\) at \(+\mathrm{bt}^2\) and $$\mathrm{R}_{\mathrm{B}}(\mathrm{t})=x \mathrm{t}-\mathrm{t}^...

A body is released from the top of a tower '\(\mathrm{H}\)' metre high. It takes \(t\) second to reach the ground. The height of the body \(\frac{t}{2}\) second after release is

Two trains, each \(30 \mathrm{~m}\) long are travelling in opposite directions with velocities \(5 \mathrm{~m} / \mathrm{s}\) and \(10 \mathrm{~m} / \mathrm{s}\). They will cross after

A shell is fired at an angle of \(30^{\circ}\) to the horizontal with velocity \(196 \mathrm{~m} / \mathrm{s}\). The time of flight is
\(\left[\sin 30^{\circ}=\frac{1}{2}=\cos 60^{\circ}\right]\)

A student is throwing balls vertically upwards such that he throws the \(2^{\text {nd }}\) ball when the \(1^{\text {st }}\) ball reaches maximum height. If he throws balls at an interval of 3 second, the maximum height of the balls is $$\l...

A driver applies the brakes on seeing the red traffic signal \(400 \mathrm{~m}\) ahead. At the time of applying the brakes, the vehicle was moving with \(15 \mathrm{~m} / \mathrm{s}\) and retarding at \(0.3 \mathrm{~m} / \mathrm{s}^2\). The...