A student is at a distance 16 m from a bus when the bus begins to move with a constant acceleration of $$9 \mathrm{~m} \mathrm{~s}^{-2}$$. The minimum velocity with which the student should run. towards the bus so as the catch it is $$\alpha \sqrt{2} \mathrm{~ms}^{-1}$$. The value of $$\alpha$$ is

An object moving along $$X$$-axis with a uniform acceleration has velocity $$\mathbf{v}=\left(12 \mathrm{cms}^{-1}\right) \hat{\mathbf{i}}$$ at $$x=3 \mathrm{~cm}$$. After 2 s if it is at $$x=-5 \mathrm{~cm}$$, then its acceleration is

$$y=\left(P t^2-Q t^3\right) \mathrm{~m}$$ is the vertical displacement of a ball which is moving in vertical plane. Then the maximum height that the ball can reach is

A car covers a distance at speed of $$60 \mathrm{~km} \mathrm{~h}^{-1}$$. It returns and comes back to the original point moving at a speed of $$v$$. If the average speed for the round trip is $$48 \mathrm{~kmh}^{-1}$$, then the magnitude of $$v$$ is