Brakes stop a train in a distance $x$. If the braking force is reduced to one-fourth of its original value,what distance will the train travel before coming to a stop?

$A$ bob of a pendulum of length $0.5 \ m$ has a speed of $6 \ ms^{-1}$ at its lowest point. Find the speed of the bob when the string of the pendulum makes $60^{\circ}$ with the vertical. (Take $g=10 \ ms^{-2}$)

$A$ knife of mass $m$ is dropped from a height $h$ onto a wooden floor. If the blade penetrates a distance $d$ into the wood,what is the average resistance offered by the wood to the knife?

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 $\text{ J}$)

$A$ small sphere of mass $m$ and radius $r$ slides down the smooth surface of a large hemispherical bowl of radius $R$. If the sphere starts sliding from rest, the total kinetic energy of the sphere at the lowest point $A$ of the bowl will be [given, moment of inertia of sphere $= \frac{2}{5} mr^2$].

$A$ sphere is suspended by a thread of length $\ell$. What minimum horizontal velocity has to be imparted to the sphere for it to reach the height of the suspension point?