A Train Is Moving At A Constant Speed V. Its Driver Observes Another Train In Front Of Him On The Same Track And Moving In The Same Direction With Constant Speed V. If The Distance Between The Train Be X, What Should Be The Minimum Retardation Of The Train So As To Avoid Collision?

A stone is dropped from a certain road. He takes 5 steps forward and 3 steps backward and so on. Each step is 1 m long and takes 1s. There is a pit on the road 11 m away from the starting point. The drunkard will fall into the pit after

A body sliding on a smooth inclined plane requires 5 s to reach the bottom, starting from rest at the top. How  much time does it take to cover one fourth the distance starting from rest at the top?

An object accelerates from rest to a velocity 27.5 m/s in 10 sec. Find the distance covered by the object during next 10 s.

Two trains, one travelling at 15 ms^-1 and other at 20 ms^-1, are heading towards one another along a straight track. Both the drivers apply brakes simultaneously when they are 500 m apart. If each train has a retardation of 1ms^-1, the separation after they stop is

A juggler keeps on moving four balls in the air throwing the balls after regular intervals. When on ball leaves his hand (speed = 20 ms^-1) the position of other balls (height in m) will be (take g = 10ms^-1)

A particle slides from rest from the topmost point of a vertical circle of radius r along a smooth chord making an angle θ with the vertical. The time of descent is

A body is thrown vertically upward from A, the top of a tower. It reaches the ground in time t₁. If it is thrown vertically downwards from A with the same speed, it reaches the ground in time t₂. If it is allowed to fall freely from A, then the time it takes the ground is given by

A parachutist drops first freely from an aeroplane for 10 s and the parachute opens out. Now the escends with a net retardation of 2.5 m/s². If the bails out of the plane at a height of 2495 m and g = 10 m/s², his velocity on reaching the ground will be

A police party is chasing a dacoit in a jeep which is moving at a constant speed v. The dacoit is on a motor cycle. When he is at a distance x from the jeep he accelerates from rest at a constant rate. Which of the following relations is true, if the police is able to catch the dacoit?