If the length of the second's hand in a stop clock is $3 \,cm$ the angular velocity and linear velocity of the tip is

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

A grinding wheel attained a velocity of $20\,rad/sec$ in $5\,sec$ starting from rest. Find the number of revolution made by the wheel

Roads are banked on curves so that

A particle moves in a circular path with decreasing speed. Choose the correct statement.

A particle at a distance of $1 m$ from the origin starts moving, such that $d r / d \theta=r$, where $r$ and $\theta$ are polar co-ordinates. Then, the angle between resultant velocity and tangential velocity is