Provided a racing car does not lose traction, the time taken by it to race from rest through a distance $x$ depends mainly on engine's power $P.$ Distance $x$ covered in time $t$ is

A block of mass $m$ is being pulled up the rough inclined plane by a man delivering constant power $P.$ The coefficient of friction between the block and the inclined is $\mu .$ The maximum speed of block during ascent is

A small ball of mass $m$ moving with speed $v(<\sqrt{2gL})$ undergoes an elastic head on collision with a stationary bob of identical mass of a simple pendulum of length $L.$ The maximum height $h,$ from the equilibrium position, to which the bob rises after. collision is

In the figure shown, a small ball hits obliquely a smooth and horizontal surface with speed $u$ whose $x$ and $y$ components are indicated. If the coefficient of restitution is $\frac{1}{2},$ then its $x$ and $y$ components $v_x$ and $v_y$ just after collision are respectively

Velocity of the ball $A$ after collision with the ball $B$ as shown in the figure is (Assume perfectly inelastic and head-on collision)