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?
Using Newton's 2nd equation, I found out the distance travelled by particle A when it was moving with an acceleration a and 2a separately and added both which came out to be 5/8 at^2. In In the second case of motion of particle B since the acceleration is changing from 2a to a I took acceleration negative. Similarly for B I got the total distance 3/8 at^2. Thus, this means particle A has covered larger distance.
Why does it happen that even though both the particles travelled with acceleration a and 2a for same time, still, particle A travelled larger distance? Please give me an answer based on intuition.