$A$ body of mass $0.5\; kg$ travels in a straight line with velocity $v=a x^{3/2}$ where $a=5\; m^{-1/2} s^{-1}$. What is the work done (in $J$) by the net force during its displacement from $x=0$ to $x=2\; m$?

$A$ spherical ball of mass $2 \text{ kg}$ falls from a height of $10 \text{ m}$ and is brought to rest after penetrating $10 \text{ cm}$ into sand. The average force exerted by sand on the ball is . . . . . . $\text{N}$. (Take $g = 10 \text{ m/s}^2$)

What does the law of conservation of energy state?

State the importance of the work-energy theorem. Is the work-energy theorem a scalar or a vector?

$A$ body of mass $5 \,kg$ is thrown vertically up with a kinetic energy of $490 \,J$. The height at which the kinetic energy of the body becomes half of the original value is (acceleration due to gravity $=9.8 \,ms^{-2}$) (in $\,m$)

$A$ body is thrown vertically upwards and reaches a maximum height $h$. What is the ratio of its kinetic energy to its potential energy at a height of $\frac{3h}{4}$?