Kinematics — JEE Main PYQs

A clock has $75\mathrm{cm},60\mathrm{cm}$ long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel x distance more than the tip of minute hand. The value of x in meter is nearly (Take $\pi =3.14$) :

The angle of projection for a projectile to have same horizontal range and maximum height is :

A body of mass M thrown horizontally with velocity $v$ from the top of the tower of height H touches the ground at a distance of 100 m from the foot of the tower. A body of mass 2M thrown at a velocity $\frac{v}{2}$ from the top of the tower of height 4H will touch the ground …

A particle moving in a straight line covers half the distance with speed 6 m/s. The other half is covered in two equal time intervals with speeds 9 m/s and 15 m/s respectively. The average speed of the particle during the motion is:

Two cars are travelling towards each other at speed of $20\mathrm{m}{\mathrm{s}}^{-1}$ each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of $2\mathrm{m}{\mathrm{s}}^{-2}$. The distance between them when they come to rest is …

A body falling under gravity covers two points A and B separated by 80 m in 2 s . The distance of upper point A from the starting point is ____ m (use $\mathrm{g}=10{\mathrm{ms}}^{-2}$)

A particle is moving in a straight line. The variation of position '$x$' as a function of time '$t$' is given as $x=(t^3-6t^2+20t+15)$ m. The velocity of the body when its acceleration becomes zero is:

A particle is moving in a circle of radius 50 cm in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at $\mathrm{t}=0$ is $4\mathrm{m}/\mathrm{s}$, the time taken to complete the first revolution will be …

Position of an ant (S in metres) moving in Y-Z plane is given by $\mathrm{S}=2{\mathrm{t}}^2\hat{\mathrm{j}}+5\hat{\mathrm{k}}$ (where t is in second). The magnitude and direction of velocity of the ant at $\mathrm{t}=1\mathrm{s}$ will be :

A particle starts from origin at $\mathrm{t}=0$ with a velocity $5\hat{\mathrm{i}}\mathrm{m}/\mathrm{s}$ and moves in $\mathrm{x}-\mathrm{y}$ plane under action of a force which produces a constant acceleration of $(3\hat{i}+2\hat{j})\mathrm{m}/{\mathrm{s}}^2$. I …

A body starts moving from rest with constant acceleration covers displacement $S_1$ in first ($p-1$) seconds and ${\mathrm{S}}_2$ in first p seconds. The displacement ${\mathrm{S}}_1+{\mathrm{S}}_2$ will be made in time:

A ball rolls off the top of a stairway with horizontal velocity u. The steps are 0.1 m high and 0.1 m wide. The minimum velocity u with which that ball just hits the step 5 of the stairway will be $\sqrt{x}$ ms${}^{-1}$ where $x=$ ______ [use $g=10$ m/s${}^2$].

The relation between time '$t$' and distance '$x$' is $t=\alpha x^2+\beta x$, where $\alpha$ and $\beta$ are constants. The relation between acceleration (a) and velocity (v) is:

A body starts falling freely from height H hits an inclined plane in its path at height $h$. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $\frac{\mathrm{H}}{\mathrm{h}}$ for which the body will take t …

Train A is moving along two parallel rail tracks towards north with speed $72\mathrm{km}/\mathrm{h}$ and train B is moving towards south with speed $108\mathrm{km}/\mathrm{h}$. Velocity of train B with respect to A and velocity of ground with respect to B are (in …

A particle initially at rest starts moving from reference point $\mathrm{x}=0$ along x-axis, with velocity $v$ that varies as $v=4\sqrt{\mathrm{x}}\mathrm{m}/\mathrm{s}$. The acceleration of the particle is ____ ${\mathrm{ms}}^{-2}$.

A particle moving in a circle of radius R with uniform speed takes time T to complete one revolution. If this particle is projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is equal to 4 R . The angle of projection $\theta$ …

A particle is moving in one dimension (along x axis) under the action of a variable force. It's initial position was 16 m right of origin. The variation of its position (x) with time (t) is given as $x=-3t^3+18t^2+16t$, where $x$ is in m and $t$ is in s. The velocity of the parti …

A particle of mass m projected with a velocity ' u ' making an angle of $30^{\circ }$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height $h$ is :

The displacement and the increase in the velocity of a moving particle in the time interval of t to $(t+1)$ s are 125 m and 50 m/s, respectively. The distance travelled by the particle in $(t+2{)}^{\text{th}}$ s is ______ m.

The trajectory of projectile, projected from the ground is given by $y=x-\frac{x^2}{20}$. Where $x$ and $y$ are measured in meter. The maximum height attained by the projectile will be.

Given below are two statements:

Statement I: Area under velocity- time graph gives the distance travelled by the body in a given time.

Statement II: Area under acceleration- time graph is equal to the change in velocity- in the given time.

In the light of given statements, cho …

Two projectiles A and B are thrown with initial velocities of $40\mathrm{m}/\mathrm{s}$ and $60\mathrm{m}/\mathrm{s}$ at angles $30^{\circ }$ and $60^{\circ }$ with the horizontal respectively. The ratio of their ranges respectively is …

As shown in the figure, a particle is moving with constant speed $\pi \mathrm{m}/\mathrm{s}$. Considering its motion from A to B, the magnitude of the average velocity is:

A particle starts with an initial velocity of $10.0{\mathrm{ms}}^{-1}$ along x-direction and accelerates uniformly at the rate of $2.0{\mathrm{ms}}^{-2}$. The time taken by the particle to reach the velocity of $60.0{\mathrm{ms}}^{-1}$ is ______.

A person travels x distance with velocity ${\mathrm{v}}_1$ and then x distance with velocity ${\mathrm{v}}_2$ in the same direction. The average velocity of the person is v , then the relation between $\mathrm{v},{\mathrm{v}}_1$ and ${\mathrm{v}}_2$ will be :

Two projectiles are projected at $30^{\circ }$ and $60^{\circ }$ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

The range of the projectile projected at an angle of $15^{\circ }$ with horizontal is 50 m. If the projectile is projected with same velocity at an angle of $45^{\circ }$ with horizontal, then its range will be:

The position-time graphs for two students A and B returning from the school to their homes are shown in figure :

(A) A lives closer to the school
(B) B lives closer to the school
(C) A takes lesser time to reach home
(D) A travels faster than B
(E) B travels faster than A

Choos …

From the v - t graph shown. the ratio of distance to displacement in 25 s of motion

A projectile fired at $30^{\circ }$ to the ground is observed to be at same height at time 3 s and 5 s after projection, during its flight. The speed of projection of the projectile is ______ ${\mathrm{ms}}^{-1}$
(Given $g=10{\mathrm{m}\mathrm{s}}^{-2}$)

A ball is thrown vertically upward with an initial velocity of $150\mathrm{m}/\mathrm{s}$. The ratio of velocity after 3 s and 5 s is $\frac{\mathrm{x}+1}{\mathrm{x}}$. The value of x is ____.

Take ( $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$ ).

Two trains ' A ' and ' B ' of length ' $l$ ' and ' $4l$ ' are travelling into a tunnel of length ' $L$ ' in parallel tracks from opposite directions with velocities $108\mathrm{km}/\mathrm{h}$ and $72\mathrm{km}/\mathrm{h}$, respectively. If train 'A' takes 35s …

A passenger sitting in a train A moving at $90\mathrm{km}/\mathrm{h}$ observes another train B moving in the opposite direction for 8 s . If the velocity of the train B is $54\mathrm{km}/\mathrm{h}$, then length of train B is :

The distance travelled by an object in time $t$ is given by $s=(2\cdot 5)t^2$. The instantaneous speed of the object at $\mathrm{t}=5\mathrm{s}$ will be :

The position of a particle related to time is given by $x=\left(5t^2-4t+5\right)\mathrm{m}$. The magnitude of velocity of the particle at $t=2\mathrm{s}$ will be :

The position vector of a particle related to time $t$ is given by
$\overrightarrow{\mathrm{r}}=\left(10\mathrm{t}\hat{\mathrm{i}}+15{\mathrm{t}}^2\hat{\mathrm{j}}+7\hat{\mathrm{k}}\right)\mathrm{m}$
The direction of net force experienced by the particle is :

A particle is moving with constant speed in a circular path. When the particle turns by an angle $90^{\circ }$, the ratio of instantaneous velocity to its average velocity is $\pi :x\sqrt{2}$. The value of $x$ will be

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : When a body is projected at an angle $45^{\circ }$, it's range is maximum.
Reason R : For maximum range, the value of $\sin 2\theta$ should be equal to one.
In th …

A projectile is projected at $30^{\circ }$ from horizontal with initial velocity $40{\mathrm{ms}}^{-1}$. The velocity of the projectile at $\mathrm{t}=2\mathrm{s}$ from the start will be:
(Given $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$)

An object moves with speed $v_1,v_2$, and $v_3$ along a line segment $\mathrm{AB},\mathrm{BC}$ and CD respectively as shown in figure. Where $\mathrm{AB}=\mathrm{BC}$ and $\mathrm{AD}=3\mathrm{AB}$, then average speed of the object will be :

A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an initial speed of $5{\mathrm{ms}}^{-1}$. Neglecting the air resistance, the speed with which the stone hits the ground will be ____ ${\mathrm{ms}}^{-1}$ (given, …

The maximum vertical height to which a man can throw a ball is 136 m . The maximum horizontal distance upto which he can throw the same ball is

A stream of a positively charged particles having $\frac{q}{m}=2\times 10^{11}\frac{C}{kg}$ and velocity ${\vec{v}}_0=3\times 10^7\hat{i}$ m/s is deflected by an electric field $1.8\hat{j}$ kV/m. The electric field exists in a region of 10 cm along x direction. Due to the el …

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 10 s is

A car travels a distance of 'x' with speed ${\mathrm{V}}_1$ and then same distance 'x' with speed ${\mathrm{V}}_2$ in the same direction. The average speed of the car is:

A uniform electric field of $10\text{ N/C}$ is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle ($\theta$) of deviation of th …

The distance travelled by a particle is related to time t as $\mathrm{x}=4{\mathrm{t}}^2$. The velocity of the particle at $\mathrm{t}=$ 5 s is .

Two objects are projected with same velocity 'u' however 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 $2^{\text{nd}}$ object will be :

A stone is projected at angle $30^{\circ }$ to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be :