The displacement of a particle is given by x=(t-2)² where x is in metres and t in seconds. The distance covered by the particle in first 4 seconds is

The position of an object moving along x-axis is given by x = a + bt², where a = 8.5 m and b = 2.5 m s^-2 and t is measured in seconds. The velocity of the object at t = 2 s is

The position x of a particle with respect to time t along x-axis is given by x=9t²-t³ where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the + x direction?

A car moving along a straight road with speed of 144 km h^-1 is brought to a stop within a distance of 200 m. How long does it take for the car to stop?

A body falling freely under gravity passes two points 30 m apart in 1 s. From what point above the upper point it began to fall? (Take g = 9.8 m s^-2)

A ball is thrown vertically upwards with a velocity of 20 m s^-1 from the top of a multistory building of 20 m high. How high will the ball rise? (Take g = 10 m s^-2)

A player throws a ball upwards with an initial speed of 30 m s^-1. How long does the ball take to return to the player’s hands? (Take g = 10 m s^-2)

Two trains A and B each of length 400 m are moving on two parallel tracks with a uniform speed 72 km h^-1 in the same direction with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m s^-2. If after 50 s, the guard of B just brushes past A, what was the original distance between them?

A man is standing on top of a building 100 m high. He throws two balls vertically, one at t = 0 and other after a time interval (less than 2 s). The later ball is thrown at a velocity of half the first. The vertical gap between first and second ball is 15 m at t = 2 s. The gap is found to remain constant. The velocities with which the balls were thrown are (Take g = 10 m s^-2)

An auto travelling along a straight road increases its speed from 30.0 m s^-1 to 50.0 m s^-1 in a distance of 180 m. If the acceleration is constant, how much time elapses while the auto moves this distance?

A motorcycle and a car start from rest from the same place at the same time and travel in the same direction. The motorcycle accelerates at 1.0 m s^-2 up to a speed of 36 km h^-1 and the car at 0.5 m s^-2 up to a speed of 54 km h^-1.The time at which the car would overtake the motorcycle is

A bird is tossing (flying to and fro) between two cars moving towards each other on a straight road. One car has speed of 27 km h^-1 while the other has the speed of 18 km h^-1. The bird starts moving from first car towards the other and is moving with the speed of 36 km h^-1 when the two cars separated by 36 km. The total distance covered by the bird is

Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km h^-1 in the direction A to B notices that a bus goes post him every 18 min in the direction of his motion, and every 6 min in the opposite direction. The period T of the bus service is

A jet airplane travelling at the speed of 500 km h^-1 ejects its products of combustion at the speed of 1500 km h^-1 relative to the jet plane. The speed of the products of combustion with respect to an observer on the ground is

A police van moving on a highway with a speed of 30 km h^-1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km h^-1. If the muzzle speed of the bullet is 150 km h^-1, with what speed does the bullet hit the thief’s car?

Two cars A and B are running at velocities of 60 km h^-1 and 45 km h^-1. What is the relative velocity of car A with respect to car B, if both are moving eastward?

On a two-lane road, car A is travelling with a speed of 36 km h^-1. Two cars B and c approach car A in opposite directions with a speed of 54 km h^-1 each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. The minimum required acceleration of car B to avoid an accident is

A ball A is dropped from a building of height 45 m, Simultaneously another identical ball B is thrown up with a speed 50 m s^-1. The relative speed of ball B w.r.t. ball A at any instant of time is (Take g = 10 m s^-2)

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

The motion of a particle is described by the equation x=a+bt² where a=15cm and b=3cm. Its instantaneous velocity at time 3 sec will be

A student is standing at a distance of 50metres from the bus. As soon as the bus starts its motion with an acceleration of 1ms^–2, the student starts running towards the bus with a uniform velocity . Assuming the motion to be along a straight road, the minimum value of , so that the students is able to catch the bus is

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