Motion in A Str...

Engine of a vehicle can give it an acceleration of $$1\;m{ s }^{ -2 }$$ and its brakes can retard it at $$3\;m{ s }^{ -1 }$$. The minimum time in which the vehicle can make a journey between stations $$A$$ and $$B$$ having a distance of $$1200\;m$$ is

A soldier jumps out from an aeroplane with a parachute. After dropping through a distance of $$19.6\ m$$, he opens the parachute and decelerates at the rate of $$1\ m{ s }^{ -2 }$$. If he reaches the ground with a speed of $$4.6\ m{ s }^{ -1 }$$, how long was he in air?

An object may have
(I) varying speed without having varying velocity.
(II) varying velocity without having varying speed.
(III) non-zero acceleration without having varying velocity.
(IV) non-zero acceleration without having varying speed.

A body travels $$200\ cm$$ in the first two seconds and $$220\ cm$$ in the next four seconds. What will be the velocity at the end of $$7^{th}$$ second from the start?

A stone is allowed to fall from the top of a tower and covers half the height of the tower in the last second of its journey. The time taken by the stone to reach the foot of the tower is

An aeroplane drops a parachutist. After covering a distance of $$40\ m$$, he opens the parachute and retards at $$2\ m{ s }^{ -2}$$. If he reaches the ground with a speed of $$2\ m{ s }^{ -1 }$$, he remains in the air for about

A particle is thrown vertically upwards from ground. It takes time $${ t }_{ 1 }$$ to reach a height $$h$$. It continues to move and takes time $${ t }_{ 2 }$$ to reach the ground. Its maximum height is

A player throws a ball upwards with an initial speed of $$29.4\ m{ s }^{ -1 }$$. The height to which the ball rises and the time taken to reach the player's hands are

A particle experiences a fixed acceleration for $$6$$ seconds after starting from rest. It cover a distance of $${ s }_{ 1 }$$ in first two seconds, $${ s }_{ 2 }$$ in the next 2 seconds and $${ s }_{ 3 }$$ in the last 2 seconds then $${ s }_{ 3 }:{ s }_{ 2 }:{ s }_{ 1 }$$ is

A body of mass $$3kg$$ falls from the multi-storeyed building $$100m$$ high and buries itself $$2m$$ deep in the sand. The time of penetration is