The distance of a particle moving on a circle of radius $12 \, m$ measured from a fixed point on the circle and measured along the circle is given by $s = 2t^3$ (in meters). The ratio of its tangential to centripetal acceleration at $t = 2 \, s$ is .........

Consider a wheel rotating around a fixed axis. If the rotation angle $\theta$ varies with time as $\theta=a t^2$,then the total acceleration of a point $A$ on the rim of the wheel is ($v$ being the tangential velocity).

$A$ particle moves along a circle of radius $3 \, m$ with its displacement given by $S = \frac{t^2}{2} + \frac{t^3}{3}$. The total acceleration at $t = 2 \, s$ is ....... $m/s^2$.

$A$ cyclist is riding with a speed of $27 \; km/h$. As he approaches a circular turn on the road of radius $80 \; m$,he applies brakes and reduces his speed at the constant rate of $0.50 \; m/s^2$. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?

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

$A$ body is moving along a circular track of radius $100 \ m$ with velocity $20 \ m/s$. Its tangential acceleration is $3 \ m/s^{2}$,then its resultant acceleration will be (in $m/s^{2}$)