$(a)$ State the law of conservation of energy.
$(b)$ What is the work done to increase the velocity of a car from $36 \, km/h$ to $72 \, km/h$ if the mass of the car is $1500 \, kg$? Does the work done by the force have a negative or a positive magnitude?
$(c)$ Where does an oscillating pendulum have maximum potential energy $(PE)$ and kinetic energy $(KE)$?

(N/A) 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.
$(b)$ Given: Mass $m = 1500 \, kg$,Initial velocity $u = 36 \, km/h = 36 \times (5/18) = 10 \, m/s$,Final velocity $v = 72 \, km/h = 72 \times (5/18) = 20 \, m/s$.
Work done $(W)$ = Change in kinetic energy = $\frac{1}{2} m (v^2 - u^2)$.
$W = \frac{1}{2} \times 1500 \times (20^2 - 10^2) = 750 \times (400 - 100) = 750 \times 300 = 225,000 \, J$ or $2.25 \times 10^5 \, J$.
Since the velocity increases,the work done is positive.
$(c)$ An oscillating pendulum has maximum potential energy $(PE)$ at its extreme positions and maximum kinetic energy $(KE)$ at its mean position.