Kinematics PYQs

When a ruler falls vertically, 5 different persons catch it with different reaction times (g = 9.8 m s⁻²): A. Person A has reaction time 0.20 s B. Person B has reaction time 0.22 s C. Person C has reaction time 0.18 s D. Person D has reaction time 0.19 s E. Person E has reaction time 0.21 s What is the correct order of the distance travelled by the ruler for each person?

In some appropriate units, time $(t)$ and position $(x)$ relation of a moving particle is given by $t = x^2 + x$. The acceleration of the particle is

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of service and the speed (assumed constant) of the buses.

A particle moving with uniform speed in a circular path maintains:

The velocity (v) – time (t) plot of the motion of a body is shown below. The acceleration (a) – time (t) graph that best suits this motion is:

A vehicle travels half the distance with speed v and the remaining distance with speed 2v. Its average speed is:

A bullet is fired from a gun at the speed of 280 m s⁻¹ in the direction 30° above the horizontal. The maximum height attained by the bullet is : (g = 9.8 m s⁻², sin 30° = 0.5)

A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity 4 m s⁻¹. The ball strikes the water surface after 4 s. The height of bridge above water surface is (Take g = 10 m s⁻²):

The ratio of the distances travelled by a freely falling body in the 1ˢᵗ, 2ⁿᵈ, 3ʳᵈ and 4ᵗʰ seconds is:

The displacement-time graphs of two moving particles make angles of 30° and 45° with the x-axis as shown in the figure. The ratio of their respective velocities is:

A ball is projected with a velocity 10 ms⁻¹, at an angle of 60° with the vertical direction. Its speed at the highest point of its trajectory will be:

A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let Sₙ be the distance travelled by the block in the interval t = n − 1 to t = n. Then, the ratio Sₙ / Sₙ₊₁ is:

A car starts from rest and accelerates at 5 m/s². At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s? (Take g = 10 m/s²)

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

A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is: (g = 10 m/s²)

A person travelling in a straight line moves with a constant velocity $v_1$ for certain distance $x$ and with a constant velocity $v_2$ for next equal distance. The average velocity $v$ is given by the relation

A particle starting from rest, moves in a circle of radius r. It attains a velocity of V₀ m/s in the nᵗʰ round. Its angular acceleration will be:

Two bullets are fired horizontally and simultaneously towards each other from rooftops of two buildings $100\ \text{m}$ apart and of same height $200\ \text{m}$, with the same velocity of $25\ \text{m/s}$ $(g = 10\ \text{m/s}^2)$. When and where will the two bullets collide?

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1$. On another day, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_2$. The time taken by her to walk up on the moving escalator will be:

Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by: $$x_P(t)=at+bt^2$$ and $$x_Q(t)=ft-t^2$$ At what time do the cars have the same velocity?

In the given figure, $a = 15\ \text{m/s}^2$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R = 2.5\ \text{m}$ at a given instant of time. The speed of the particle is:

A projectile is fired from the surface of the earth with a velocity of $5\,\text{m s}^{-1}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3\,\text{m s}^{-1}$ at the same angle follows a trajectory which is identical to the trajectory of the projectile fired from earth. The value of the acceleration due to gravity on the planet is (in $\text{m s}^{-2}$) given $g = 9.8\,\text{m s}^{-2}$.

A particle is moving such that its position coordinates $(x, y)$ are $(2\,\text{m}, 3\,\text{m})$ at time $t = 0$, $(6\,\text{m}, 7\,\text{m})$ at time $t = 2\,\text{s}$ and $(13\,\text{m}, 14\,\text{m})$ at time $t = 5\,\text{s}$. Average velocity vector $\left(\vec{v}_{\text{av}}\right)$ from $t = 0$ to $t = 5\,\text{s}$ is:

The velocity of a projectile at the initial point $A$ is $(2\hat{i} + 3\hat{j})\ \mathrm{m/s}$. Its velocity (in $\mathrm{m/s}$) at point $B$ is

A particle covers half of its total distance with speed v₁ and the rest half distance with speed v₂. Its average speed during the complete journey is:

A projectile is fired at an angle of 45° with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection is:

A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are $e_1$ and $e_2$ respectively, then the percentage error in the estimation of g is

The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is

A particle moves in the $xy$-plane according to the rule $$x = a\sin\omega t$$ $$y = a\cos\omega t$$ The particle follows

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is $S_1$ and that covered in the first 20 seconds is $S_2$ then:

A bus is moving with a speed of $10\,\mathrm{m\,s^{-1}}$ on a straight road. A scooterist wishes to overtake the bus in $100\,\mathrm{s}$. If the bus is at a distance of $1\,\mathrm{km}$ from the scooterist, with what speed should the scooterist chase the bus?

The distance travelled by a particle starting from rest and moving with an acceleration 4/3 ms⁻² in the third second is

A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms⁻¹ to 20 ms⁻¹ while passing through a distance 135 m in t second. The value of t is

A particle shows distance-time curve as given in the figure. The maximum instantaneous velocity of the particle is around the point

A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be

For angles of projection of a projectile at angles (45° − θ) and (45° + θ), the horizontal ranges described by the projectile are in the ratio of:

A particle moves along a straight line OX. At a time t (in seconds), the distance x (in metres) of the particle from O is given by x = 40 + 12t − t³. How long would the particle travel before coming to rest?

A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 s for every circular lap. The average velocity and average speed for each circular lap respectively are:

Two bodies, A (of mass 1 kg) and B (of mass 3 kg), are dropped from heights of 16 m and 25 m respectively. The ratio of the time taken by them to reach the ground is:

If a vector $$2\hat{i}+3\hat{j}+8\hat{k}$$ is perpendicular to the vector $$4\hat{j}-4\hat{i}+\alpha\hat{k}$$ then the value of $\alpha$ is: