$(a)$ What is meant by mechanical energy? State its two forms. State the law of conservation of energy. Give an example in which we observe a continuous change of one form of energy into another and vice-versa.
$(b)$ Calculate the amount of work required to stop a car of $1000 \, kg$ moving with a speed of $72 \, km \, h^{-1}$.

(B) Mechanical energy is the sum of kinetic energy $(KE)$ and potential energy $(PE)$ of an object. Its two forms are kinetic energy and potential energy. The law of conservation of energy states that energy can neither be created nor destroyed; it can only be transformed from one form to another. An example is a simple pendulum: at the mean position,the energy is entirely kinetic,while at the extreme positions,it is entirely potential. As the pendulum oscillates,energy continuously converts between kinetic and potential forms.
$(b)$ Given: Mass $m = 1000 \, kg$,initial velocity $u = 72 \, km \, h^{-1} = 72 \times (5/18) \, m \, s^{-1} = 20 \, m \, s^{-1}$,final velocity $v = 0 \, m \, s^{-1}$.
Work done = Change in kinetic energy = $\frac{1}{2} m (v^2 - u^2)$.
Work done = $\frac{1}{2} \times 1000 \times (0^2 - 20^2) = 500 \times (-400) = -200,000 \, J = -2 \times 10^5 \, J$.
The negative sign indicates that work is done against the motion of the car.