Kinematics — JEE Main PYQs

A Tennis ball is released from a height $h$ and after freely falling on a wooden floor it rebounds and reaches height $\frac{\mathrm{h}}{2}$. The velocity versus height of the ball during its motion may be represented graphically by:
(graphs are drawn schematically and on not to …

Starting from the origin at time $t=0$, with initial velocity $5\hat{j}{\mathrm{ms}}^{-1}$, a particle moves in the $x$ - y plane with a constant acceleration of $(10\hat{\mathrm{i}}+4\hat{\mathrm{j}}){\mathrm{ms}}^{-2}$. At time t , its coordinates are ( 20 …

The speed verses time graph for a particle is shown in the figure. The distance travelled (in m) by the particle during the time interval $\mathrm{t}=0$ to $\mathrm{t}=5\mathrm{s}$ will be ____

Ship A is sailing towards north - east with velocity $\vec{v}=30\hat{\mathrm{i}}+50\hat{\mathrm{j}}\mathrm{km}/\mathrm{hr}$ where $\hat{\mathrm{i}}$ points east and $\hat{j}$, north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing toward …

A particle starts from origin O from rest and moves with a uniform acceleration along the positive x-axis. Identify all figures that correctly represent the motion qualitatively. ($a=$ acceleration, $v=$ velocity, $x=$ displacement, $t=$ time)

The stream of a river is flowing with a speed of $2\mathrm{km}/\mathrm{h}$. A swimmer can swim at a speed of $4\mathrm{km}/\mathrm{h}$. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?

A ball is thrown vertically up (taken as +z -axis) from the ground. The correct momentumheight ( $p-h$ ) diagram is:

Two guns A and B can fire bullets at speed $1\mathrm{km}/\mathrm{s}$ and $2\mathrm{km}/\mathrm{s}$ respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on …

A particle moves from the point $(2.0\hat{\mathrm{i}}+4.0\hat{\mathrm{j}})\mathrm{m}$, at $\mathrm{t}=0$ with an initial velocity $(5.0\hat{\mathrm{i}}+4.0\hat{\mathrm{j}}){\mathrm{ms}}^{-1}$. It is acted upon by a constant force which produces a constant acceleration …

A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance R from it. If ${\mathrm{t}}_1$ and ${\mathrm{t}}_2$ are the values of the time taken by it to hit the target in two possible ways, the product …

The trajectory of a projectile near the surface of the earth is given as $y=2x-9x^2$. If it were launched at an angle ${\theta }_0$ with speed $v_0$, then $(g=10\mathrm{m}{\mathrm{s}}^{-2})$:

A plane is inclined at an angle $\alpha =30^{\circ }$ with respect to the horizontal. A particle is projected with a speed $u=2{\mathrm{ms}}^{-1}$, from the base of the plant, making an angle $\theta =15^{\circ }$ with respect to the plane as shown in the figure. The distance from th …

A body is projected at $t=0$ with a velocity $10{\mathrm{ms}}^{-1}$ at an angle of $60^0$ with the horizontal. The radius of curvature of its trajectory at $t=1\mathrm{s}$ is R. Neglecting air resistance and taking acceleration due to gravity $g=10{\mathrm{ms}}^{-2}$, the rad …

A particle is moving along a circular path with a constant speed of $10{\mathrm{ms}}^{-1}$. What is the magnitude of the change in velocity of the particle, when it moves through an angle of $60^{\circ +}$ around the centre of the circle?

A passenger train of length 60 m travels at a speed of $80\mathrm{km}/\mathrm{hr}$. Another freight train of length 120 m travels at a speed of $30\mathrm{km}/\mathrm{hr}$. The ratio of times taken by the passenger train to completely cross the freight train when:
(i) the …

Two particles are projected from the same point with the same speed u such that they have the same range R , but different maximum heights, ${\mathrm{h}}_1$ and ${\mathrm{h}}_2$. Which of the following is correct?

A particle is moving with speed $v=v\sqrt{x}$ along positive $x$-axis. Calculate the speed of the particle at time $\mathrm{t}=\mathrm{t}$ (assume that the particle is at origin at $\mathrm{t}=0$).

Two particles $A,B$ are moving on two concentric circles of radii $R_1$ and $R_2$ with equal angular speed $\omega$. At $\mathrm{t}=0$, their positions and direction of motion are shown in the figure :

The relative velocity $\overrightarrow{V_A}-\overrightarrow{V_B}$ at …

The position of a particle as a function of time $t$, is given by $x(t)=at+b{t}^2-c{t}^3$ where $a$, $b$ and $c$ are constants. When the particle attains zero acceleration, then its velocity will be:

The position vector of a particle changes with time according to the relation $\vec{r}(t)=15t^2\hat{i}+(4-20t^2)\hat{j}$. What is the magnitude of the acceleration at $t=1$?

In a car race on straight road, car A takes a time ' t ' less than car B at the finish and passes finishing point with a speed ' v ' more than that of car B . Both the cars start from rest and travel with constant acceleration ${\mathrm{a}}_1$ and ${\mathrm{a}}_2$ respectively. T …

The position co-ordinates of a particle moving in a 3-D coordinates system is given by


The speed of the particle is:

A particle is moving with a velocity $\vec{v}=K(y\hat{i}+x\hat{j})$, where K is a constant. The general equation for its path is:

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?

Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of $10\mathrm{m}/\mathrm{s}$ and $40\mathrm{m}/\mathrm{s}$ respectively. Which of the following graph best represents the time variation of relative position of the second stone …

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:

A projectile is given an initial velocity of $(\hat{i}+2\hat{j})\mathrm{m}/\mathrm{s}$, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$, the equation of its trajectory is:

A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be

Two cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$, respectively. Their speeds are such that they make complete circles in the same time $t$. The ratio of their centripetal acceleration is

An object, moving with a speed of $6.25\text{ m/s}$, is decelerated at a rate given by :

where v is the instantaneous speed. The time taken by the object, to come to rest, would be :

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is :

A particle is moving with velocity $\vec{v}=K(y\hat{i}+x\hat{j})$, where $K$ is a constant. The general equation for its path is

A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of 'P' is such that it sweeps out a length $s=t^3+5$, where $s$ is in metres and $t$ is in seconds. The radius of the path is 20 m. The acceleration of 'P' when …

For a particle in uniform circular motion the acceleration $\vec{a}$ at a point $P(R,\theta )$ on the circle of radius $R$ is (here $\theta$ is measured from the x-axis)

A particle has an initial velocity $3\hat{i}+4\hat{j}$ and an acceleration of $0.4\hat{i}+0.3\hat{j}$. Its speed after 10 s is

Consider a rubber ball freely falling from a height $\mathrm{h}=4.9\mathrm{m}$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time the height as funct …

A body is at rest at x=0. At t=0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x=0 moving in the positive x direction with a constant speed. The position of the first body is given by $x_1(t)$ after t …

A particle is projected at $60^{\circ }$ to the horizontal with a kinetic energy K. The kinetic energy at the highest point is

The velocity of a particle is $v=v_0+gt+f{t}^2$. If its position is $x=0$ at $t=0$, then its displacement after unit time ($t=1$) is

A particle located at $x=0$ at time $t=0$, starts moving along the positive x-direction with a velocity '$v$' that varies as $v=\alpha \sqrt{x}$. The displacement of the particle varies with time as

A projectile can have the same range $R$ for two angles of projection. If $t_1$ and $t_2$ be the times of flights in the two cases, then the product of the two time of flights is proportional to

The relation between time $t$ and distance $x$ is $t=a{x}^2+bx$ where $a$ and $b$ are constants.

The acceleration is

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

A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at $2\mathrm{m}/{\mathrm{s}}^2$. He reaches the ground with a speed of $3\mathrm{m}/\mathrm{s}$. At what height, did he bail out?

A ball is released from the top of a tower of height $h$ metres. It takes T seconds to reach the ground. What is the position of the ball in T/3 seconds?

A projectile can have the same range $R$ for two angles of projection. If $T_1$ and $T_2$ be the time of flights in the two cases, then the product of the two time of flights is directly proportional to

Which of the following statements is false for a particle moving in a circle with a constant angular speed?

An automobile travelling with speed of $60\mathrm{km}/\mathrm{h}$, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e $120\mathrm{km}/\mathrm{h}$, the stopping distance will be

A ball is thrown from a point with a speed $v_0$ at an angle of projection $\theta$. From the same point and at the same instant person starts running with a constant speed $v_0/2$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angl …