An unloaded bus can be stopped by applying brakes on a straight road after covering a distance $x$. Suppose the passengers add $50 \%$ of its weight as the load and the braking force remains unchanged,how far will the bus go after the application of the brakes? (Velocity of the bus in both cases is the same.)

$A$ body of mass $0.5\, kg$ travels on a straight-line path with velocity $v = (3x^2 + 4)\, m/s$. The net work done by the force during its displacement from $x = 0$ to $x = 2\, m$ is $.......J$.

$A$ 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.

Two monkeys with the same mass stand on a branch at height $h$ above the horizontal jungle floor. Monkey $A$ steps off the branch holding the end of an inextensible rope of length $L$ whose other end is tied to another branch at height $H$,lets go at the bottom of the swing,and falls freely to the floor,as shown below. Monkey $B$ steps off and falls straight downward. Then,neglecting air resistance but not the tension in the rope,the total work $W$ done on each monkey and the speed $v$ with which each hits the floor are as follows:

The velocity at which the $6 \text{ kg}$ mass (shown in the figure) strikes the ground when it is released from a height of $6 \text{ m}$ above the ground is . . . . . . $\text{m/s}$. Assume the pulley is massless and the string is light and inextensible. (Take $g = 10 \text{ m/s}^2$)

$A$ body of mass $1 \ kg$ is under a force, which causes a displacement given by $x = \frac{t^3}{3}$ (in $m$). Find the work done by the force in the first second (in $J$).