Kinematics — JEE Main PYQs

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R . If A and B reached the maximum height …

Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by $X_P(t)=\alpha t+\beta t^2$ and ${\mathrm{X}}_{\mathrm{Q}}(\mathrm{t})=\mathrm{ft}-{\mathrm{t}}^2$. At what time, both the buses have same velocity?

For a particle in uniform circular motion, the acceleration $\overrightarrow{\mathrm{a}}$ at any point $\mathrm{P}(\mathrm{R},\theta )$ on the circular path of radius $R$ is (when $\theta$ is measured from the positive x -axis and v is uniform speed) :

A force on an object of mass 100 g is $(10\hat{\mathrm{i}}+5\hat{\mathrm{j}})$ N. The position of that object at $\mathrm{t}=2$ s is $(\mathrm{a}\hat{\mathrm{i}}+\mathrm{b}\hat{\mathrm{j}})$ m after starting from rest. The value of $\frac{a}{b}$ will be

Motion of a particle in x-y plane is described by a set of equations $x=4\sin (\omega t)$ m and $y=4\cos (\omega t)$ m. The path of the particle will be:

Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction at an interval of 3s with the same initial velocity of $35\mathrm{m}/\mathrm{s}$, then these balls collide at a height of ______ m. (Take …

If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?

A bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a:

A butterfly is flying with a velocity $4\sqrt{2}\mathrm{m}/\mathrm{s}$ in North-East direction. Wind is slowly blowing at $1\mathrm{m}/\mathrm{s}$ from North to South. The resultant displacement of the butterfly in 3 seconds is :

In a spring gun having spring constant $100\mathrm{N}/\mathrm{m}$ a small ball 'B' of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0.05 m. There should be a box placed at a distance 'd' on the ground so that the ball falls in it. If …

A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time $t_1$. If he remains stationary on a moving escalator then the escalator takes him up in time $t_2$. The time taken by him to walk up on the moving escalator wi …

A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec . The number of rotations made in the process is ____.

A player kicks a football with an initial speed of $25{\mathrm{ms}}^{-1}$ at an angle of $45^{\circ }$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion? (Take $\mathrm{g}=10{\mathrm{ms}}^{-2}$)

Water drops are falling from a nozzle of a shower onto the floor, from a height of 9.8 m . The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when t …

An engine of a train, moving with uniform acceleration, passes the signal - post with velocity $u$ and the last compartment with velocity $v$. The velocity with which middle point of the train passes the signal post is :

A particle is moving with uniform speed along the circumference of a circle of radius of radius $R$ under the action of a central fictitious force F which is inversely proportional to ${\mathrm{R}}^3$. Its time period of revolution will be given by:

A boy pushes a box of mass 2 kg with a force $\vec{F}=(20\hat{i}+10\hat{j})\mathrm{N}$ on a frictionless surface. If the box was initially at rest, then ____ m is displacement along the x -axis after 10 s .

A huge circular arc of length 4.4 ly subtends an angle ' 4 s ' at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second?
Given : $1\mathrm{ly}=9.46\times 10^{15}\mathrm{m}$ …

If the velocity of a body related to displacement $x$ is given by $v=\sqrt{5000+24x}\mathrm{m}/\mathrm{s}$, then the acceleration of the body is ______

The trajectory of a projectile in a vertical plane is $\mathrm{y}=\alpha \mathrm{x}-\beta {\mathrm{x}}^2$, where $\alpha$ and $\beta$ are constants and $x\&y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of pro …

A scooter accelerates from rest for time $t_1$ at constant rate $a_1$ and then retards at constant rate $a_2$ for time $t_2$ and comes to rest. The correct value of $\frac{t_1}{t_2}$ will be:

A particle is moving with constant acceleration 'a'. Following graph shows $v^2$ versus $x$ (displacement) plot. The acceleration of the particle is ______ $\mathrm{m}/{\mathrm{s}}^2$.

A helicopter is flying horizontally with a speed ' $v$ ' at an altitude ' $h$ ' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?

A ball is thrown up with a certain velocity so that it reaches a height '$h$'. Find the ratio of the two different times of the ball reaching $\frac{\mathrm{h}}{3}$ in both the directions.

A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is t seconds, the total distance traveled is :

The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of revolutions by the truck engine during this time is ______ (Assuming the acceleration to be uniform) .

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at $4^{\text{th}}$ second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap? (Take $\mathrm{g}=9.8\mathrm{m}/{\mathrm{s}}^2$)

A balloon was moving upwards with a uniform velocity of $10m/s$. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around :
(takes the …

The relation between time $t$ and distance $x$ for a moving body is given as $t=m{x}^2+nx$, where $m$ and $n$ are constants. The retardation of the motion is : (Where $v$ stands for velocity)

The instantaneous velocity of a particle moving in a straight line is given as $\mathrm{v}=\alpha \mathrm{t}+\beta {\mathrm{t}}^2$, where $\alpha$ and $\beta$ are constants. The distance travelled by the particle between 1 s and 2 s is :

A swimmer wants to cross a river from point A to point B . Line $AB$ makes an angle of $30^{\circ }$ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle $\theta$ with the line $AB$ should be
____ ${}^{\circ }$, so th …

The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ }$ and $48^{\circ }$ with the horizontal are ${\mathrm{R}}_1,{\mathrm{R}}_2$ and ${\mathrm{H}}_1,{\mathrm{H}}_2$ respectively. Choose the correct option:

The velocity- displacement graph describing the motion of a bicycle is shown in the figure. The acceleration-displacement graph of the bicycle's motion is best described by:

A mosquito is moving with a velocity $\vec{v}=0.5t^2\hat{i}+3t\hat{j}+9\hat{k}\mathrm{m}/\mathrm{s}$ and accelerating in uniform conditions. What will be the direction of mosquito after 2 s ?

A swimmer can swim with velocity of $12\mathrm{km}/\mathrm{h}$ in still water. Water flowing in a river has velocity 6 $\mathrm{km}/\mathrm{h}$. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank j …

The velocity -displacement graph of a particle is shown in the figure. The acceleration - displacement graph of the same particle is represented by :

The velocity of a particle is $v=v_0+gt+{\mathrm{Ft}}^2$. Its position is $\mathrm{x}=0$ at $\mathrm{t}=0$; then its displacement after time ($\mathrm{t}=1$) is:

A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to $\frac{81}{100}$ of the height through which it falls. Find the average speed of the ball. (Take $\mathrm{g}=10{\mathrm{ms}}^{-2}$)

The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by:

A person is swimming with a speed of $10\mathrm{m}/\mathrm{s}$ at an angle of $120^0$ with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is 'x' $\mathrm{m}/\mathrm{s}$. The value of 'x' to the nearest integer …

A particle is moving along the $x$-axis with its coordinate with time ' $t$ ' given by $x(t)=10+8t-3t^2$. Another particle is moving along the $y$-axis with its coordinate a function of time given by $y(t)=5-8t^3$. At $t=1\mathrm{s}$, the speed of the second …

A particle moves such that its position vector $\vec{r}(t)=\cos \omega t\hat{i}+\sin \omega t\hat{j}$ where $\omega$ is a constant and $t$ is time. Then which of the following statements is true for the velocity $\vec{v}(t)$ and acceleration $\vec{a}(t)$ of the particle:

A ball is dropped form the top of a 100 m high tower on a planet. In the last $\frac{1}{2}\mathrm{s}$ before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity (in ${\mathrm{ms}}^{-2}$) near the surface on that planet is ____.

A particle starts from the origin at $t=0$ with an initial velocity of $3.0\hat{i}\mathrm{m}/\mathrm{s}$ and moves in the $x$ - $y$ plane with a constant acceleration $(6.0\hat{i}+4.0\hat{j})\mathrm{m}/{\mathrm{s}}^2$. The $x$-coordinate of the particle at t …

The distance $x$ covered by a particle in one dimensional motion varies with time $t$ as $x^2=a{t}^2+bt+c$. If the acceleration of the particle depends on $x$ as $x^{-n}$, where $n$ is an integer, the value of $n$ is ____.

The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point S is at 4.333 seconds. The total distance covered by the body in 6 s is:

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v , he sees that rain drops are coming at an angle $60^{\circ }$ from the horizontal. On further increasing the speed of the car to $(1+\beta )\mathrm{v}$, this angle change …

A balloon is moving up in air vertically above a point A on the ground. When it is at a height ${\mathrm{h}}_1$, a girl standing at a distance d (point B) from A (see figure) sees it at the angle $45^0$ with respect to the vertical. When the balloon climbs up a future heigh …

A helicopter rises from rest on the ground vertically upwards with a constant acceleration g . A food packet is dropped from the helicopter when it is at a height h . The time taken by the packet to reach the ground is close to [ $g$ is the acceleration due to gravity]:

A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in units of ${\mathrm{ms}}^{-2}$) is of the order of: