Kinematics — JEE Main PYQs

A 0.4 kg mass takes 8 s to reach ground when dropped from a certain height 'P' above surface of earth. The loss of potential energy in the last second of fall is ______ J. [Take $g=10m/{\mathrm{s}}^2$]

A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of …

A vehicle travels 4 km with speed of $3\mathrm{km}/\mathrm{h}$ and another 4 km with speed of $5\mathrm{km}/\mathrm{h}$, then its average speed is :

A stone tied to 180 cm long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is $\frac{1936}{x}$ ms⁻². The value of x ______. (Take $\pi =\frac{22}{7}$)

Match Column-I with Column-II :

Choose the correct answer from the options given below:

A horse rider covers half the distance with $5\mathrm{m}/\mathrm{s}$ speed. The remaining part of the distance was travelled with speed $10\mathrm{m}/\mathrm{s}$ for half the time and with speed $15\mathrm{m}/\mathrm{s}$ for other half of the time. The mean speed of t …

The initial speed of a projectile fired from ground is $u$. At the highest point during its motion, the speed of projectile is $\frac{\sqrt{3}}{2}u$. The time of flight of the projectile is:

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following {Assume negligible air friction}

The speed of a swimmer is $4$ km h${}^{-1}$ in still water. If the swimmer makes his strokes normal to the flow of river of width 1 km, he reaches a point 750 m down the stream on the opposite bank.

The speed of the river water is _____ km h${}^{-1}$.

A body is moving with constant speed, in a circle of radius 10 m. The body completes one revolution in 4 s. At the end of 3rd second, the displacement of body (in m) from its starting point is:

Two bodies are projected from ground with same speeds $40{\mathrm{ms}}^{-1}$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of $60^{\circ }$, with horizontal then sum of the maximum heights …

For a body projected at an angle with the horizontal from the ground, choose the correct statement.

For a train engine moving with speed of $20{\text{ms}}^{-1}$, the driver must apply brakes at a distance of 500 m before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with sp …

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is

A ball is released from a height $h$. If $t_1$ and $t_2$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_1$ and $t_2$.

A NCC parade is going at a uniform speed of $9\mathrm{km}/\mathrm{h}$ under a mango tree on which a monkey is sitting at a height of 19.6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is : …

At time $\mathrm{t}=0$ a particle starts travelling from a height $7\hat{\mathrm{z}}\mathrm{cm}$ in a plane keeping z coordinate constant. At any instant of time it's position along the $x$ and $y$ directions are defined as $3t$ and $5t^3$ respectively. At …

A ball is thrown vertically upwards with a velocity of $19.6{\mathrm{ms}}^{-1}$ from the top of a tower. The ball strikes the ground after 6 s. The height from the ground up to which the ball can rise will be $\left(\frac{\mathrm{k}}{5}\right)\mathrm{m}$. The value of k is ..... …

A bullet is shot vertically downwards with an initial velocity of $100\mathrm{m}/\mathrm{s}$ from a certain height. Within 10 s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time …

A ball of mass m is thrown vertically upward. Another ball of mass 2m is thrown at angle $\theta$ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is $\frac{1}{x}$. The value of $x$ is …

A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be : (Given $\cos 135^{\circ }=-0.7$)

A car is moving with speed of $150\mathrm{km}/\mathrm{h}$ and after applying the brake it will move 27 m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ______ m distance.

Two projectiles are thrown with same initial velocity making an angle of $45^{\circ }$ and $30^{\circ }$ with the horizontal respectively. The ratio of their respective ranges will be

A body of mass 10 kg is projected at an angle of $45^{\circ }$ with the horizontal. The trajectory of the body is observed to pass through a point $(20,10)$. If T is the time of flight, then its momentum vector, at time $\mathrm{t}=\frac{\mathrm{T}}{\sqrt{2}}$, is ____
[ …

A block 'A' takes 2 s to slide down a frictionless incline of $30^{\circ }$ and length ' $l$ ', kept inside a lift going up with uniform velocity ' $v$ '. If the incline is changed to $45^{\circ }$, the time taken by the block, to slide down the incline, will be approximate …

Two inclined planes are placed as shown in figure. A block is projected from the Point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top Point B at a height 10 m. After reaching the Point B the block slides down on inclined plane BC. …

A ball is projected from the ground with a speed $15{\mathrm{ms}}^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal, then $\tan \theta$ will be equal to

A particle is moving in a straight line such that its velocity is increasing at $5{\mathrm{ms}}^{-1}$ per meter. The acceleration of the particle is __________ ${\mathrm{ms}}^{-2}$ at a point where its velocity is $20{\mathrm{ms}}^{-1}$.

Two projectile thrown at $30^0$ and $45^0$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is

If the initial velocity in horizontal direction of a projectile is unit vector $\hat{\mathrm{i}}$ and the equation of trajectory is $\mathrm{y}=5\mathrm{x}(1-\mathrm{x})$. The y component vector of the initial velocity is ____ $\hat{\mathrm{j}}$
(Take …

A ball is spun with angular acceleration $\alpha =6{\mathrm{t}}^2-2\mathrm{t}$ where t is in second and $\alpha$ is in rads ${}^{-2}$. At $\mathrm{t}=0$, the ball has angular velocity of 10 rads ${}^{-1}$ and angular position of 4 rad. The most appropriate expression for t …

A car covers AB distance with first one-third at velocity ${\mathrm{v}}_1{\mathrm{ms}}^{-1}$, second one-third at ${\mathrm{v}}_2{\mathrm{ms}}^{-1}$ and last one-third at ${\mathrm{v}}_3{\mathrm{ms}}^{-1}$. If …

When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10 m in t s, the distance travelled by the toy in the next t s will be :

A person can throw a ball upto a maximum range of 100 m . How high above the ground he can throw the same ball?

A ball is projected vertically upward with an initial velocity of $50{\mathrm{ms}}^{-1}$ at $\mathrm{t}=0\mathrm{s}$. At $\mathrm{t}=2\mathrm{s}$, another ball is projected vertically upward with same velocity.

At $\mathrm{t}=$ _____ s, second ball will meet the firs …

Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at $t=0$ s. Ball B is thrown vertically down with an initial velocity '$u$' at $t=2$ s. After a certain time, both balls meet 100 m above the ground. Find the value of '$u$' in …

An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero ?

A fighter jet is flying horizontally at a certain altitude with a speed of 200 m/s. When it passes directly overhead an anti-aircraft gun, bullet is fired from the gun, at an angle $\theta$ with the horizontal, to hit the jet. If the bullet speed is 400 m/s, the value of $\theta$ …

A ball of mass 0.5 kg is dropped from the height of 10 m. The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is ____ m. (Use g = 10 m/s²).

A projectile is launched at an angle '$\alpha$' with the horizontal with a velocity $20{\mathrm{ms}}^{-1}$. After 10 s, its inclination with horizontal is '$\beta$'. The value of $\tan \beta$ will be : $\left(\mathrm{g}=10{\mathrm{ms}}^{-2}\right)$

A girl standing on road holds her umbrella at $45^{\circ }$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $15\sqrt{2}km{h}^{-1}$, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl …

A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h . Find the ratio of the times in which it is at height $\frac{\mathrm{h}}{3}$ while going up and coming down respectively.

If $\mathrm{t}=\sqrt{\mathrm{x}}+4$, then ${\left(\frac{\mathrm{dx}}{\mathrm{dt}}\right)}_{\mathrm{t}=4}$ is:

A ball is projected with kinetic energy E, at an angle of $60^{\circ }$ to the horizontal. The kinetic energy of this ball at the highest point of its flight will become :

An object is projected in the air with initial velocity $u$ at an angle $\theta$. The projectile motion is such that the horizontal range R , is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity rem …

A projectile is projected with velocity of $25\mathrm{m}/\mathrm{s}$ at an angle $\theta$ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of $\theta$ will be : [use …

From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1.5 s. A third ball released, from the rest from the same location, will reach th …

An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use $g=10$ ms${}^{-2}$]

A body is projected from the ground at an angle of $45^{\circ }$ with the horizontal. Its velocity after 2 s is $20{\mathrm{ms}}^{-1}$. The maximum height reached by the body during its motion is ______ m. (use $\mathrm{g}=10{\mathrm{ms}}^{-2}$)