$A$ car travelling at $80 \ km/h$ can be stopped at a distance of $60 \ m$ by applying brakes. If the same car travels at $160 \ km/h$ and the same braking force is applied,the stopping distance is: (in $m$)

$A$ small block slides down from rest at point $A$ on the surface of a smooth cylinder,as shown. At point $B$,the block falls off (leaves) the cylinder. The equation relating the angles $\theta_1$ and $\theta_2$ is given by

$A$ cricket ball of mass $0.15 \, kg$ is thrown vertically up by a bowling machine so that it rises to a maximum height of $20 \, m$ after leaving the machine. If the part pushing the ball applies a constant force $F$ on the ball and moves a distance of $0.2 \, m$ while launching the ball,the value of $F$ (in $N$) is $(g = 10 \, m/s^2)$.

The velocity-time graph for a body of mass $10 \ kg$ is shown in the figure. The work done on the body in the first two seconds of motion is:

$A$ simple pendulum is released from point $A$ as shown in the figure. If $m$ and $l$ represent the mass of the bob and the length of the pendulum respectively,the gain in kinetic energy at point $B$ is:

The work-energy theorem is valid in the presence of: