$A$ body of mass $0.25 \ kg$ travels along a straight line from $x=0$ to $x=2 \ m$ with a speed $v=k x^{3/2}$ where $k=2$ $SI$ units. The work done by the net force during this displacement is: (in $J$)

$A$ body is released from a height of $30 \ m$ vertically downwards. The speed of the body at which potential energy is twice that of kinetic energy is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)

The displacement-time graph of a particle moving in a straight line is as shown in the figure. Select the correct alternative.

$A$ body of mass $2 \, kg$ is projected vertically upwards with a kinetic energy of $490 \, J$. At what height will its kinetic energy become half of its initial value? $(g = 9.8 \, m/s^2)$

$A$ bead of mass $\frac{1}{2} \, kg$ starts from rest from point $A$ to move in a vertical plane along a smooth fixed quarter ring of radius $5 \, m$,under the action of a constant horizontal force $F = 5 \, N$ as shown. The speed of the bead as it reaches point $B$ is ................ $m/s$. [Take $g = 10 \, m/s^2$]

Brakes stop a train in a distance $x$. If the braking force is reduced to one-fourth of its original value,what distance will the train travel before coming to a stop?