A particle starts performing circular motion in a circle of radius $1 \mathrm{m}$ at $t=0.$ Its speed $v$ varies with time $t$  as, $v=4t \mathrm{m} {\mathrm{s}}^{-1}.$ where $t$ is in seconds. If $a_r$ and $a_t$ are the radial and tangential acceleration of the particle respectively, then

Two particles $A$ and $B$ are at rest at separation of $160 \mathrm{m}.$ Both the particle starts moving at $t=$ $0.$ Particle A moves in a straight line perpendicular to initial position $AB$ with constant acceleration of $3 \mathrm{m} {\mathrm{s}}^{-2}.$ Particle $B$ moves in such a way that it always aims towards $A$ and moves with speed increasing at constant rate of $5 \mathrm{m} {\mathrm{s}}^{-2}.$ Then

A particle is projected from ground to ground and its path is as shown in the figure. Points $A$ and $B$ are at same horizontal level and points $C$ and $D$ are at another same horizontal level. Separation between line $AB$ and $CD$ is $5 \mathrm{m}.$ If particle takes time $t_1$ to go from $A$ to $B$ and time $t_2$ from $C$ to $D,$ then is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A stone is projected horizontally with velocity $v$  from a building of height $h.$ It hits the inclined plane perpendicularly as shown in figure. Then