The Displacement Of A Body From A Reference Point, Is Given By            Where x is In Metres And t in Seconds. This Shown That The Body Is

The area under the velocity-time graph between any two instants t = t₁and t = t₂ gives the distance covered in time 

A particle is given a displacement of 4 m in the x-y plane. If the x-component of the displacement vector is 2 m, the y-component will be

A car, starting from rest, accelerates at a constant rate of 5 ms^–2 for some time. It then retards at a constant rate of 10 ms^–2 and finally comes to rest. If the total taken is 6 s, What is the maximum speed attained by the car? 

A body, starting from rest, moves in a straight line with a constant acceleration a for a time interval t during which it travels a distance s₁. If continues to move with the same acceleration for the next time interval tduring which it travels a distance s₂. The relation between s₁ and s₂ is

A stone is dropped from a height of 125 m. If g = 10 ms^–2, what is the ratio of the distances traveled by it during the first and the last second of its motion? 

A body, moving in a straight line, with an initial velocity u and a constant acceleration a, covers a distance of 40 m in the 4^th second and a distance of 60 m in the 6^th second. The values of u and a respectively are    

A simple pendulum is hanging from the ceiling of a compartment of a train. It is observed that the string is inclined towards the rear of the train. If follows that the train 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 was nv, what must be the deceleration of the car to stop it in the same distance and in the same time?

A car is moving at a certain speed. The minimum distance over which it can be stopped is x. If the speed of the car is doubled, what will be the minimum distance over which the car can be stopped during the same time? 

A ball is thrown vertically downward with a velocity u from the top of a tower. It strikes the ground with a velocity 3u. The time taken by the ball to reach the ground is given by