Kinematics — JEE Main PYQs

A projectile is thrown upward at an angle $60^{\circ }$ with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is $45^{\circ }$ with the horizontal. The initial speed of the projectile is ______ m/s.

A river of width 200 m is flowing from west to east with a speed of $18\mathrm{km}/\mathrm{h}$. A boat, moving with speed of $36\mathrm{km}/\mathrm{h}$ in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for thi …

An object is projected with kinetic energy K from a point A at an angle $60^{\circ }$ with the horizontal. The ratio of the difference in kinetic energies points B and C to that at point A (see figure), in the absence of air friction is :

A block is sliding down on an inclined plane of slope $\theta$ and at an instant $t=0$ this block is given an upward momentum so that it starts moving up on the inclined surface with velocity $u$. The distance $(S)$ travelled by the block before its velocity become zero, …

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with $3\mathrm{m}/{\mathrm{s}}^2$. At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is …

A bead $P$ sliding on a frictionless semi-circular string $(ACB)$ and it is at point $S$ at $\mathrm{t}=0$ and at this instant the horizontal component of its velocity is $v$. Another bead $Q$ of the same mass as $P$ is ejected from point $A$ at $\mathrm{t}=0$ …

A boy thrown a ball into air at $45^{\circ }$ from the horizontal to land it on a roof of a building of height H. If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of H is ______ m.
($\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$)

Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is ______ m.
( …

The velocity (v) - Distance (x) graph is shown in figure. Which graph represents acceleration (a) versus distance ( x ) variation of this system?

A particle starts moving from time $\mathrm{t}=0$ and its coordinate is given as $\mathrm{x}(\mathrm{t})=4{\mathrm{t}}^3-3\mathrm{t}$.
A. The particle returns to its original position (origin) 0.866 units later
B. The particle is 1 unit away from origin at its turning point …

The two projectiles are projected with the same initial velocities at the $15^{\circ }$ and $30^{\circ }$ with respect to the horizontal. The ratio of their ranges is $1:x$. The value of $x$ is

Two cars A and B are moving in the same direction along a straight line with speeds $100\mathrm{km}/\mathrm{h}$ and $80\mathrm{km}/\mathrm{h}$, respectively such that car A is moving ahead of car B . A person in car B throws a stone with a speed v so that it hits the car …

If x and y coordinates of a projectile as a function of time $(t)$ are given as $24t$ and $43.6t-4.9t^2$, respectively, then the angle (in degrees) made by the projectile with horizontal when $\mathrm{t}=2\mathrm{s}$ is $\_\_\_\_$ .

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m . The speed of the bullets from the gun is ______ $\mathrm{m}/\mathrm{s}$. (take $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$)

From 18 m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is ______ m.
(Take $g=10$ m/s${}^2$ and neglect the air resistance)

The velocity $(v)$ versus time $(t)$ plot of a particle is shown in the figure, for a time interval of 40s. The total distance travelled by the particle and the average velocity during this period are, respectively ______

A gas balloon is going up with a constant velocity of $10\mathrm{m}/\mathrm{s}$. When this balloon reached a height of 75 m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is
____ m …

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of $R$ is ____ m. (Take $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$)

Two masses of 3.4 kg and 2.5 kg are accelerated from an initial speed of $5\mathrm{m}/\mathrm{s}$ and $12\mathrm{m}/\mathrm{s}$, respectively. The distances traversed by the masses in the $5^{\text{th }}$ second are 104 m and 129 m, respectively. The ratio of their momen …

The velocity of a particle is given as $\overrightarrow{\mathrm{v}}=-x\hat{\mathrm{i}}+2y\hat{\mathrm{j}}-z\hat{\mathrm{k}}\mathrm{m}/\mathrm{s}$. The magnitude of acceleration at point $(1,2,4)$ is ____ $\mathrm{m}/{\mathrm{s}}^2$.

A particle is rotating in a circular path and at any instant its motion can be described as $\theta =\frac{5t^4}{40}-\frac{t^3}{3}$. The angular acceleration of the particle after 10 seconds is ____ $\mathrm{rad}/{\mathrm{s}}^2$.

A particle is projected at an angle of $30^{\circ }$ from horizontal at a speed of $60\mathrm{m}/\mathrm{s}$. The height traversed by the particle in the first second is ${\mathrm{h}}_0$ and height traversed in the last second, before it reaches the maximum height, is $h_1$. …

The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is $\_\_\_\_$ km .

A ball having kinetic energy KE, is projected at an angle of $60^{\circ }$ from the horizontal. What will be the kinetic energy of ball at the highest point of its flight?

Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time $\mathrm{t}=0$, for the first time. The maximum possible number of crossing(s) (inc …

Two projectiles are fired with same initial speed from same point on ground at angles of $\left(45^{\circ }-\alpha \right)$ and ( $45^{\circ }+\alpha$ ), respectively, with the horizontal direction. The ratio of their maximum heights attained is :

The maximum speed of a boat in still water is $27\mathrm{km}/\mathrm{h}$. Now this boat is moving downstream in a river flowing at $9\mathrm{km}/\mathrm{h}$. A man in the boat throws a ball vertically upwards with speed of $10\mathrm{m}/\mathrm{s}$. Range of the ball …

The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between $\mathrm{t}=0$ to $\mathrm{t}=4\mathrm{s}$ ?

The position vector of a moving body at any instant of time is given as $\overrightarrow{\mathrm{r}}=\left(5{\mathrm{t}}^2\hat{\mathrm{i}}-5\mathrm{t}\hat{\mathrm{j}}\right)\mathrm{m}$. The magnitude and direction of velocity at $\mathrm{t}=2\mathrm{s}$ is,

A sportsman runs around a circular track of radius $r$ such that he traverses the path ABAB. The distance travelled and displacement, respectively, are

Which of the following curves possibly represent one-dimensional motion of a particle ?
(A) (see graph)
(B) (see graph)
(C) (see graph)
(D) (see graph)

Choose the correct answer from the options given below :

The angle of projection of a particle is measured from the vertical axis as $\varphi$ and the maximum height reached by the particle is ${\mathrm{h}}_{\mathrm{m}}$. Here ${\mathrm{h}}_{\mathrm{m}}$ as function of $\varphi$ can be presented as

A particle is projected with velocity $u$ so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as $\frac{n{u}^2}{25g}$, where value of $n$ is :
(Given '$g$' is the acceleration due to gravity).

A particle moves along the x-axis and has its displacement $x$ varying with time $t$ according to the equation
$x=c_0(t^2-2)+c(t-2{)}^2$
where $c_0$ and c are constants of appropriate dimensions. Then, which of the following statements is correct?

If $\overrightarrow{\mathrm{L}}$ and $\overrightarrow{\mathrm{P}}$ represent the angular momentum and linear momentum respectively of a particle of mass ' m ' having position vector …

A helicopter flying horizontally with a speed of $360\mathrm{km}/\mathrm{h}$ at an altitude of 2 km , drops an object at an instant. The object hits the ground at a point O , 20 s after it is dropped. Displacement of ' O ' from the position of helicopter where the object wa …

Two projectiles are fired from ground with same initial speeds from same point at angles ($45^{\circ }+\alpha$) and ($45^{\circ }-\alpha$) with horizontal direction. The ratio of their times of flights is

Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ are the total flying times of first and second ball, resp …

The displacement x versus time graph is shown below.
(A) The average velocity during 0 to 3 s is $10\mathrm{m}/\mathrm{s}$
(B) The average velocity during 3 to 5 s is $0\mathrm{m}/\mathrm{s}$
(C) The instantaneous velocity at $\mathrm{t}=2\mathrm{s}$ is …

A person travelling on a straight line moves with a uniform velocity ${\mathrm{v}}_1$ for a distance x and with a uniform velocity $v_2$ for the next $\frac{3}{2}x$ distance. The average velocity in this motion is $\frac{50}{7}\mathrm{m}/\mathrm{s}$. If …

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in $t_1$. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in $t_2$. Time required to reach the ground, if it is dropped f …

A particle moves in a straight line so that its displacement x at any time t is given by ${\mathrm{x}}^2=1+{\mathrm{t}}^2$. Its acceleration at any time t is ${\mathrm{x}}^{-\mathrm{n}}$ where $\mathrm{n}=$ ______.

A cyclist starts from the point P of a circular ground of radius 2 km and travels along its circumference to the point S. The displacement of a cyclist is :

A bus moving along a straight highway with speed of $72\text{km/h}$ is brought to halt within 4 s after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is ________ m.

A body travels 102.5 m in ${\mathrm{n}}^{\text{th }}$ second and 115.0 m in $(\mathrm{n}+2{)}^{\text{th }}$ second. The acceleration is :

The co-ordinates of a particle moving in $x-y$ plane are given by :
$x=2+4t,y=3t+8t^2$.
The motion of the particle is :

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9 m and completes 120 revolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in $\mathrm{m}/{\mathrm{s}}^2$ ) :

The maximum height reached by a projectile is 64 m. If the initial velocity is halved, the new maximum height of the projectile is ____ m.

A body moves on a frictionless plane starting from rest. If ${\mathrm{S}}_{\mathrm{n}}$ is distance moved between $\mathrm{t}=\mathrm{n}-1$ and t $=n$ and $S_{n-1}$ is distance moved between $t=n-2$ and $\mathrm{t}=\mathrm{n}-1$, then the ratio …

A train starting from rest first accelerates uniformly up to a speed of $80\mathrm{km}/\mathrm{h}$ for time t, then it moves with a constant speed for time 3t. The average speed of the train for this duration of journey will be (in $\mathrm{km}/\mathrm{h}$) :