$A$ particle moves in a circular path of radius $r$ with speed $v.$ It then increases its speed to $2v$ while travelling along the same circular path. The centripetal acceleration of the particle has changed by a factor of

$A$ particle moves in a circular path of radius $R$ with an angular velocity $\omega = a - bt$,where $a$ and $b$ are positive constants and $t$ is time. The magnitude of the acceleration of the particle after time $t = \frac{2a}{b}$ is:

$A$ car is moving on a circular path of radius $600\,m$ such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete the first quarter of a revolution,if it is moving with an initial speed of $54\,km/h$,is $t(1 - e^{-\pi/2})\,s$. The value of $t$ is $.............$.

$A$ car moves with a speed of $30 \, m/s$ on a circular path of radius $500 \, m$. If its tangential acceleration is $2 \, m/s^2$,what is the magnitude of the total acceleration of the car in $m/s^2$?

$A$ 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?

$A$ car is travelling with linear velocity $v$ on a circular road of radius $r$. If it is increasing its speed at the rate of $a \ m/s^2$,then the resultant acceleration will be