The centripetal acceleration is given by

The tangential acceleration of a particle moving in a circle of radius $1 \ m$ varies with time $t$ as shown in the graph (initial velocity of the particle is zero). The time after which the total acceleration of the particle makes an angle of $30^{\circ}$ with the radial acceleration is:

In the given figure,$a = 15 \, m s^{-2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R = 2.5 \, m$ at a given instant of time. The speed of the particle is ........ $m/s$.

The acceleration of a train travelling with a speed of $400 \, m/s$ as it goes round a curve of radius $160 \, m$ is:

$A$ car is travelling with linear velocity '$V$' on a circular road of radius '$r$'. If its velocity is increasing at a rate of '$a$' $ms^{-2}$, then the resultant acceleration will be

$A$ point object moves along an arc of a circle of radius $R$. Its velocity depends upon the distance covered $s$ as $v=K \sqrt{s}$,where $K$ is a constant. If $\theta$ is the angle between the total acceleration and tangential acceleration,then