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A body starts from rest and accelerates uniformly at a rate α for a certain duration, then decelerates uniformly at a rate β until it comes to rest after t seconds. If the maximum velocity vₘₐₓ is given by vₘₐₓ = (αβ)/(α + β), what is the total distance covered by the body?

1. The total distance covered by the body is (αβt²)/(2α + 2β).
2. The total distance covered by the body is (αβt²)/(α + β).
3. The total distance covered by the body is (αβt)/(α + β).
4. The total distance covered by the body is (αβt²)/(αβ).

Correct answer: The total distance covered by the body is (αβt²)/(2α + 2β).

Solution

The given problem involves uniformly accelerated motion followed by uniform retardation. Using the equations of motion and the given conditions, the distance traveled can be derived as (αβt²)/(2α + 2β).

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