If the time taken to bring a ball to rest from a certain velocity $v$ is reduced to half,what will be the changes in values of
$(a)$ Initial and final momentum.
$(b)$ Change of momentum.
$(c)$ Rate of change of momentum.

(C) Initial momentum $p_i = mv$ and final momentum $p_f = 0$. Since $m$ and $v$ remain constant,there is no change in initial and final momentum.
$(b)$ Change of momentum $\Delta p = p_f - p_i = 0 - mv = -mv$. Since the magnitude of change depends only on initial and final states,there is no change.
$(c)$ Rate of change of momentum is given by $F = \frac{\Delta p}{t}$. If time $t$ is reduced to half $(t' = t/2)$,the new rate of change of momentum $F' = \frac{\Delta p}{t/2} = 2 \times \frac{\Delta p}{t} = 2F$. Thus,the rate of change of momentum is doubled.