The co-ordinates of a moving particle at any time ' $t$ ' are given by $x=\alpha t^3$ and $y=\beta t^3$ where $\alpha$ and $\beta$ are constants. The speed of the particle at time ' $t$ ' is given by

A ball is released from the top of a tower of height Hm . It takes T second to reach the ground. The height of the ball from the ground after $\frac{T}{4}$ second is

Two cars start from a point at the same time in a straight line and their positions are represented by $x_1(t)=a t+b t^2$ and $x_2(t)=F t-t^2$. At what time do the cars have the same velocity?

A bullet is fired on a target with velocity V . Its velocity decreases from V to $\mathrm{V} / 2$. When it penetrates 30 cm in a target. Through what thickness it will penetrate further in the target before coming to rest?