Consider an object of mass $m$ connected with an ideal spring of spring constant $k$. Show that the speed and the $KE$ will be maximum at equilibrium position. Get an expression for the maximum speed.

Consider the collision shown in Fig. between two billiard balls with equal masses. The player wants to 'sink' the target ball in a corner pocket, which is at an angle ${\theta }_2=30°$. Assume an elastic collision. Neglect friction and rotational motion. Find ${\theta }_1$

Discuss elastic collision in two dimensions briefly.

The work done by the force for $x=1 \mathrm{m}$ to $x=4 \mathrm{m}$ for the following force-position graph is