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 half and a for the second half. Which particle has covered larger distance?

Question

Philoid · Accepted Answer

We know that the slope of a line in velocity-time graph gives acceleration (a) of the particle. Therefore, from the given data, we have

Therefore, the velocity-time (v-T) graph is shown below

Now, from the above graph,

Distance covered by Particle A=Area under curve for particle A

Distance covered by Particle B=Area under curve for particle B

Therefore, Distance covered by particle B is greater than distance covered by particle A.