$A$ bullet of mass $0.04\; kg$ moving with a speed of $90\; m/s$ enters a heavy wooden block and is stopped after a distance of $60\; cm$. What is the average resistive force exerted by the block on the bullet (in $; N$)?

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.)

The bob of a pendulum was released from a horizontal position. The length of the pendulum is $10 \ m$. If it dissipates $10 \%$ of its initial energy against air resistance,the speed with which the bob arrives at the lowest point is : [Use $g = 10 \ ms^{-2}$]

$A$ truck accelerates from speed $v$ to $2v$. The work done during this process is:

$A$ 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 $J$)

$A$ particle of mass $m$ is moving along a circle of radius $R$ such that its tangential acceleration $a_t$ varies with distance covered $x$ as $a_t = \alpha x^2$,where $\alpha$ is a constant. The kinetic energy $K$ of the particle varies with the distance as $K = \beta x^c$,where $\beta$ and $c$ are constants. The values of $\beta$ and $c$ are: