Fill in the blanks:
$(a)$ If the momentum of an object is doubled,its kinetic energy becomes ........
$(b)$ For a perfectly inelastic collision,the coefficient of restitution $e$ $=$ .....
$(c)$ An appliance with $1\,kW$ power consumes $1\,kWh$ of energy in ....... time.

(A) The kinetic energy $K$ is related to momentum $p$ by the formula $K = \frac{p^2}{2m}$. Since $K \propto p^2$,if the momentum is doubled $(p_2 = 2p_1)$,the new kinetic energy $K_2 = (2)^2 K_1 = 4K_1$. Thus,it becomes four times.
$(b)$ By definition,for a perfectly inelastic collision,the objects stick together after the collision,resulting in a coefficient of restitution $e = 0$.
$(c)$ Energy $E = P \times t$. Given $E = 1\,kWh$ and $P = 1\,kW$,the time $t = \frac{E}{P} = \frac{1\,kWh}{1\,kW} = 1\,hour$.