The length of second's hand in a watch is $1 \,cm.$ The change in velocity of its tip in $15\, seconds$ is

A car is moving with speed $30$ $m/\sec $ on a circular path of radius $500\, m$. Its speed is increasing at the rate of $2m/{\sec ^2},$ What is the acceleration of the car ........ $m/sec^2$

A man standing on the roof of a house of height $h$ throws one particle vertically downwards and another particle horizontally with the same velocity $u$. The ratio of their velocities when they reach the earth's surface will be

The angular acceleration of a body, moving along the circumference of a circle, is :

When an object is shot from the bottom of a long smooth inclined plane kept at an angle $60^{\circ}$ with horizontal. it can travel a distance $\mathrm{x}_{1}$ along the plane. But when the inclination is decreased to $30^{\circ}$ and the same object the shot with the same velocity, it can travel $x_{2}$ distance. Then $x_{1}: x_{2}$ will be

If speed of a particle moving in a circle of radius $2\,m$ is given as $v = 2t + 2$, then its centripetal acceleration after $1\, s$ will be   ......... $m/s^2$