If position vector of a particle is $\left[ {(3t)\widehat i\, + \,(4{t^2})\widehat j} \right]$ , then obtain its velocity vector for $2\,s$.

What can be the angle between velocity and acceleration for the motion in two or three dimension ?

A particle is moving with velocity $\vec v = K(y\hat i + x\hat j)$ where $K$ is a constant. The general equation for its path is

Two balls are thrown horizontally from the top of a tower with velocities $v_1$ and $v_2$ in opposite directions at the same time. After how much time the angle between velocities of balls becomes $90^o$ ?

Two boys are standing at the ends $A$ and $B$ of a ground where $AB = a$. The boy at $B$ starts running in a direction perpendicular to $AB$ with velocity ${v_1}.$ The boy at $A$ starts running simultaneously with velocity $v$ and catches the other boy in a time $t$, where $t$ is

In the figure shown, the two projectiles are fired simultaneously. The minimum distance between them during their flight is  ........ $m$