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A particle begins from rest and covers a distance x under constant acceleration. It then moves through a distance 2x at constant speed, and finally covers a distance 3x under constant retardation, coming to rest at the end. If the entire motion is along one straight line, what is the ratio of the average velocity to the maximum velocity?

1. 2/5
2. 3/5
3. 4/5
4. 6/7

Correct answer: 3/5

Solution

The average velocity is calculated by dividing the total distance traveled by the total time taken. In this scenario, the particle covers a total distance of 6x and the time taken can be derived from the equations of motion for each segment, leading to an average velocity that is 3/5 of the maximum velocity achieved during the motion.

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