$A$ child is swinging on a swing. The minimum and maximum heights of the swing from the earth's surface are $0.75\,m$ and $2\,m$ respectively. The maximum velocity of this swing is ............. $m/s$.

$A$ balloon filled with helium rises against gravity,increasing its potential energy. The speed of the balloon also increases as it rises. How do you reconcile this with the law of conservation of mechanical energy? You can neglect viscous drag of air and assume that the density of air is constant.

The position $x$ of a particle moving in one dimension under the influence of a constant force is given by $t = \sqrt{x} + 3$, where $x$ is in meters and $t$ is in seconds. Find the work done in the first $6$ seconds. (in $\text{ J}$)

$A$ body of mass $2 \, kg$ is thrown vertically upwards with a velocity of $4 \, m/s$. At what height will its kinetic energy be half of its initial value (in $, m$)? (Take $g = 10 \, m/s^2$)

$A$ lorry and a car moving with the same kinetic energy $(K.E.)$ are brought to rest by applying the same retarding force. Then:

$A$ particle is released from a height $H$. At a certain height,its kinetic energy is half of its potential energy with reference to the surface of the earth. The height and speed of the particle at that instant are respectively: