A point $P$ moves in counter clock wise direction on a circular path as shown in figure.  The movement of $'P'$ is such that it sweeps out a length $S = t^3 + 5$, where $'S'$ is in meter and $t$ is in seconds. The radius of the path is $20\, m$. The acceleration of $'P'$ when $t = 2\, sec$. is nearly     ......... $m/s^2$

If the instantaneous velocity of a particle projected as shown in figure is given by $v =a \hat{ i }+(b-c t) \hat{ j }$, where $a, b$, and $c$ are positive constants, the range on the horizontal plane will be

For a particle in uniform circular motion, the acceleration $\overrightarrow{ a }$ at any point $P ( R , \theta)$ on the circular path of radius $R$ is (when $\theta$ is measured from the positive $x\,-$axis and $v$ is uniform speed)

A projectile is projected with speed $u$ of an angle of $60^o$ with horizontal from the foot of an inclined plane. If the projectile hits the inclined plane horizontally, the range on inclined plane will be :-

The $x-t$ graph of a particle moving along a straight line is shown in figure The distance-time graph of the particle is correctly shown by

The $x-t$ graph of a particle moving along a straight line is shown in figure The $a-t$ graph of the particle is correctly shown by