Motion Test - 4...

The two ends of a train moving with constant acceleration pass a certain point with velocities $$u$$ and $$v$$. The velocity with which the middle point of the train passes the same point is

A stone is thrown vertically upwards. When the particle is at one-half its maximum height, its speed is $$10  { m }/{ s }$$, then maximum height attained by particle is $$\left( g=10  { m }/{ { s }^{ 2 } } \right)$$:

A stone is thrown upwards with a velocity $$v$$ from the top of a tower. It reaches the ground with a velocity $$3v$$. What is the height of the tower?

A ball is dropped downwards, after $$1$$ sec another ball is dropped downwards from the same point. What is the distance between them after $$3$$ sec? (Take $$g=10ms^{-2}$$)

A stone thrown vertically upwards with a speed of $$5{ m }/{ s }$$ attains a height $${ H }_{ 1 }$$. Another stone thrown upwards from the same point with a speed of $$10{ m }/{ s }$$ attains a height $${ H }_{ 2 }$$. The correct relation between $${ H }_{ 1 }$$ and $${ H }_{ 2 }$$ is

Similar balls are thrown vertically each with a velocity $$20\ { m }/{ s }$$, one on the surface of earth and the other on the surface of moon. What will be ratio of the maximum heights attained by them? $$($$Acceleration on moon $$=\dfrac{g}{6}\ m / s^2$$ approximately, where $$g$$ is gravitational acceleration due to earth$$)$$

In uniform circular motion

If you were to throw a ball vertically upward with an initial velocity of $$50 \; ms^{-1}$$, approximately how long would it take for the ball to return to your hand? Assume air resistance is negligible. (Given $$g=10\; ms^{-2}$$)

A stone thrown upward with a speed $$u$$ from the top of the tower reaches the ground with a velocity $$3u$$. The height of the tower is

A ball released from a height falls $$5 m$$ in one second. In 4 seconds it falls through (Take $$g=10ms^{-2}$$):