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A car accelerates from rest at a constant rate α for some time after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t seconds, the total distance travelled is:

1. 4αβ/(α + β) t²
2. 2αβ/(α + β) t²
3. αβ/(2(α + β)) t²
4. 4αβ/(α + β) t²

Correct answer: αβ/(2(α + β)) t²

Solution

The correct option is derived from the kinematic equations for uniformly accelerated motion. The car accelerates and then decelerates, and the total distance can be expressed as the sum of the distances covered during both phases, leading to the formula αβ/(2(α + β)) t², which accounts for the average speed during the entire motion.

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