Equations of Kinematics

A car passes three points A, B and C at $3$ m/s, $6$ m/s and $9$ m/s respectively in a straight line with uniform acceleration. If distance $AB = 60$ m then find the distance BC.

A body moving with uniform acceleration travel $16$ m in the third second of its motion and $24$ m in the fifth second of its motion. The velocity of the body in $10$ second is

Two bodies A and B move in same straight line starting from same position. Body A moves with constant velocity ' u ' and body B moves with constant acceleration ' $a$ '. When their velocities become equal, the distance between them is

A car moving at a speed ' v ' is stopped in a certain distance when the brakes produce a deceleration ' $a$ '. If the speed of the car is ' $nv$ ', what must be the deceleration of the car to stop it in the same distance and in the same time?

A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered by the body in the $n$th second of its motion to the total distance travelled in n second is

A body travelling with uniform acceleration crosses two points A and B with velocities $20\text{ m/s}$ and $30\text{ m/s}$ respectively. The speed of the body at mid point of A and B is (nearly)

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

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

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

A body starts moving from rest with constant acceleration covers displacement $S_1$ in first $(p-1)$ seconds and $S_2$ in first $p$ seconds. The displacement $S_1 + S_2$ will be made in time:

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

A bullet is fired on a target with velocity V. Its velocity decreases from V to $V/2$. When it penetrates 30 cm in a target. Through what thickness it will penetrate further in the target before coming to rest?

A driver applies the brakes on seeing the red traffic signal 400 m ahead. At the time of applying brakes, the vehicle was moving with $15\text{ m/s}$ and retarding at $0.3\text{ m/s}^2$. The distance of the vehicle from the traffic light one minute after application of brakes is

A body moves on a frictionless plane starting from rest. If $S_n$ is distance moved between $t = n - 1$ and $t = n$ and $S_{n-1}$ is distance moved between $t = n - 2$ and $t = n - 1$, then the ratio $\frac{S_{n-1}}{S_n}$ is $\left(1 - \frac{2}{x}\right)$ for $n = 10$. The value of $x$ is __________.

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

Two bodies $A$ and $B$ start from the same point at the same instant and move along a straight line. Body $A$ moves with uniform acceleration $a$ and body $B$ moves with uniform velocity $v$. They meet after time $t$. The value of $t$ is

A bullet is fired on a target with velocity '$V$'. Its velocity decreases from '$V$' to '$V/2$' when it penetrates $30\text{ cm}$ in a target. Through what thickness it will penetrate further in the target before coming to rest?

For a train engine moving with speed of $20\text{ ms}^{-1}$, the driver must apply brakes at a distance of 500 $\text{m}$ 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 speed $\sqrt{x}\text{ ms}^{-1}$. The value of $x$ is ____________.

(Assuming same retardation is produced by brakes)

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

Two trucks A and B are approaching each other on a straight path with the velocities of $16\text{ m/s}$ and $20\text{ m/s}$ respectively. When they are $200\text{ m}$ apart their drivers see each other and applies the breaks simultaneously. If the truck A decelerates with $2\text{ m/s}^2$ and truck B decelerates with $4\text{ m/s}^2$, what is the distance between them when they finally stop?

A car is moving with speed of $150\text{ km/h}$ and after applying the brake it will move $27\text{ m}$ 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.

The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is:

A scooter accelerates from rest for time t1 at constant rate a1 and then retards at constant rate a2 for time t2 and comes to rest. The correct value of $\frac{t_1}{t_2}$ will be:

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:

Two bodies '$A$' and '$B$' start from the same point at the same instant and move along a straight line. 'A' moves with uniform acceleration (a) and 'B' moves with uniform velocity (V). They meet after time 't'. The value of 't' is

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 travelled is:

A driver applies the brakes on seeing the red traffic signal $400\text{ m}$ ahead. At the time of applying the brakes, the vehicle was moving with $15\text{ m/s}$ and retarding at $0.3\text{ m/s}^2$. The distance covered by the vehicle from the traffic light 1 minute after the application of brakes is

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 $\frac{S_n}{S_{n+1}}$ is:

A moving body is covering distances which are proportional to square of the time. Then, the acceleration of the body is

A particle moves from the point $\left(2.0\hat{i} + 4.0\hat{j}\right)$ m, at t = 0, with an initial velocity $\left(5.0\hat{i} + 4.0\hat{j}\right)$ ms${}^{-1}$. It is acted upon by a constant force which produces a constant acceleration $\left(4.0\hat{i} + 4.0\hat{j}\right)$ ms${}^{-2}$. What is the distance of the particle from the origin at time 2 s?

In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed '$v$' more than that of car B. Both the cars start from rest and travel with constant acceleration a1 and a2 respectively. Then '$v$' is equal to:

An automobile, travelling at $40$ km/h, can be stopped at a distance of $40$ m by applying brakes. If the same automobile is travelling at $80$ km/h, the minimum stopping distance, in metres, is (assume no skidding):

A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration 2 m/s2 and the car has acceleration 4 m/s2. The car will catch up with the bus after a time of:

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is S1 and that covered in the first 20 seconds is S2, then

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

The distance travelled by a particle starting from rest and moving with an acceleration $\frac{4}{3}$ m s${}^{-2}$, in the third second is

A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate $\frac{f}{2}$ to come to rest. If the total distance traversed is 15 S, then

An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e 120 km/h, the stopping distance will be

A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the same car is moving at a speed of 100 km/hr, the minimum stopping distance is

Speeds of two identical cars are $u$ and $4u$ at the specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is:

A car moving with a speed of $40\text{ km/h}$ can be stopped by applying brakes after atleast $2\text{ m}$. If the same car is moving with a speed of $80\text{ km/h}$, what is the minimum stopping distance?

If a car at rest accelerates uniformly to a speed of 144 km/h in 20 sec, it covers a distance of

The velocity of train increases uniformly from 20 km/h to 60 km/h in 4 hours. The distance travelled by the train during this period is

A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ and comes to rest. If total time elapsed is $t$, then maximum velocity acquired by car will be

A body starts from rest, what is the ratio of the distance travelled by the body during the 4th and 3rd second?

A car is moving along a straight road with a uniform acceleration. It passes through two points $P$ and $Q$ separated by a distance with velocity 30 km/h and 40 km/h respectively. The velocity of the car midway between $P$ and $Q$ is