Motion Test - 3...

The ratio of the heights from which two bodies are dropped is 3 : 5 respectively. The ratio of their final velocities is?

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 balloonist is ascending at a velocity of $$12\ m{ s }^{ -1 }$$. A packet is dropped from it when it is at height of $$65 \ m$$ from the ground. Time taken by the packet to reach the ground is

When a ball is $$h$$ metre high from a point $$O$$, its velocity is $$v$$. When it is $$h\ m$$ below $$O$$, its velocity is $$2v$$. Find the maximum height from $$O$$ it will acquire.

The displacement - time graphs of two bodies $$A$$ and $$B$$ are $$OP$$ and $$OQ$$ respectively. Velocities of A and B are related as 

A point moves rectilinearly in one direction. Above figure shows the distance $$s$$ traversed by the point as a function of the time $$t$$. Using the plot, find the maximum velocity.

The first stage of the rocket launches a satellite to a height of $$50\ km$$ and velocity attained is $$6000\ km{ h }^{ -1 }$$ at which point its fuel exhausted. How high the rocket will reach (Take $$g=10\ m/s^2$$ and assume $$g$$ is constant up to for rocket's entire journey?

At which instant do the two cars have the same velocity?

When a ball is thrown up vertically with a velocity $${ v }_{ 0 }$$ it reaches a height $$h$$. If one wishes to triple the maximum height then the ball be thrown with a velocity