A particle is performing uniform circular motion with speed $\frac{\pi \mathrm{m}}{\mathrm{s}}.$ If radius of circular path is $2 \mathrm{m}$ then magnitude of average velocity of particle in time interval, $\Delta t=1.5 \mathrm{s}$ is

A swimmer can swim at speed $v_0$ in still water. River flow speed is variable given by $v_r=\frac{v_{0}y}{a},$ where $y$ is the distance from one bank of the river and $a$ is width of river. If swimmer crosses the river in shortest possible time then drift of the swimmer in this case is

A swimmer $A$ who want to reach directly at point $B$ on the other bank of the river swims with minimum possible speed with respect to river and reaches directly at point $B.$ If width of the river is $\mathrm{w}$ and river flows with velocity $v_0,$ then time in which swimmer crosses the river, is

A mouse is at a distance of $d$ from a cat. Both start running with constant equal speed $v_0$ in such a way that mouse moves in a straight line perpendicular to initial line joining cat and mouse, and cat always moves aiming at mouse. Separation between them when both move on the same line is

A particle is moving in $X-Y$ plane on path $y=x^2-$ $2x+5.$ Its $x$ component of velocity is constant and is equal to $5 \mathrm{m} {\mathrm{s}}^{-1}.$ Acceleration of the particle at $x=2 \mathrm{m}$ is

A ball is thrown with velocity $\overrightarrow{u}=(3\hat{i}+4\hat{j})\mathrm{m} {\mathrm{s}}^{-1}$ towards a wall, where it hits at height $h_1$ at time $t_1$ after the launch.

Another ball is projected from same point with velocity $\overrightarrow{u}=(3\hat{i}+5\hat{j})\mathrm{m} {\mathrm{s}}^{-1}$ towards the wall where it hits at height $h_2$ at time $t_2$ after the launch. Then