Question

Two particles A and B start from rest and move for equal time on a straight line. The particle A has an acceleration a for the first half of the total time and 2a for the second half. The particle B has an acceleration 2a for the first and a for the second half. Which particle has covered larger distance?

Answer 1

From the velocity–time graph, we have:
Distance covered by A = ($\frac{1}{2}\times \frac{t}{2}\times \frac{at}{2}+\frac{1}{2}\times \frac{t}{2}\times \frac{at}{2}+\frac{t}{2}\times \frac{at}{2})=\frac{a{t}^2}{2}$
Distance covered by B = $(\frac{1}{2}\times at\times \frac{t}{2}+at\times \frac{t}{2}+\frac{1}{2}\times \frac{at}{2}\times \frac{t}{2})=\frac{7}{8}a{t}^2$
∴ Distance covered by A < Distance covered by B