When a rubber-band is stretched by a distance $x$, it exerts a restoring force of magnitude $F=ax+b{x}^2$ where a and b are constants. The work done in stretching the un stretched rubber-band by $L$ is

Water falls from a height of  $60 \mathrm{m}$ at the rate of  $15 \mathrm{kg}/\mathrm{s}$ to operate a turbine. The losses due to frictional forces are $10\%$  of energy. How much power is generated by the turbine? $(\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2)$.

An engine develops $10 \mathrm{kW}$ of power. The time it will take in lifting a mass of  $200 \mathrm{kg}$ to a height of $40 \mathrm{m}. (\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2)$ is:

A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time $t$ is proportional to:

An athlete in the Olympic Games covers a distance of $100 \mathrm{m}$ in $10 \mathrm{s}$. His kinetic energy can be estimated to be in the range

A shell explodes in mid-air. It's total:

A body is moving at a speed of $1.0 {\mathrm{ms}}^{-1}$. A force  $F$ is required to stop it within a distance $x$. If the speed of the body increases to $3.0 {\mathrm{ms}}^{-1}$, then the force required to stop it within the same distance $x$ will be:

The relation between the displacement $x$ and the time $t$ for a body of mass $2 \mathrm{kg}$ moving under the action of a force is given by $x=t^3/3$, where $x$ is in metre and $t$ in second. The work done (in joule) by the body in the first two seconds is:

A ball of mass $0.2 \mathrm{kg}$ is thrown vertically upward by applying a force by hand. If the hand moves $0.2 \mathrm{m}$ while applying the force and the ball goes up to $2 \mathrm{m}$ height further, find the magnitude of the force. Consider $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.