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     ......... $m/s^2$

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)

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

A body of mass $m$ is suspended from a string of length $l$. What is minimum horizontal velocity that should be given to the body in its lowest position so that it may complete one full revolution in the vertical plane with the point of suspension as the centre of the circle

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