A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate β and comes to rest. If the total time elapsed is t , then the maximum velocity acquired by the car is

Question

A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate β and comes to rest. If the total time elapsed is t , then the maximum velocity acquired by the car is, ( α 2 − β 2 α β ) t, ( α 2 + β 2 α β ) t, ( α + β ) t α β, α β t α + β

MARKS App · Accepted Answer

Let us draw the v − t graph of the given situation. Initially it accelerates uniformly from rest. Hence, it is a straight line. v max = 0 + α t 1 ⇒ t 1 = v max α 0 = v max − β t 2 ⇒ t 2 = v max β In Figure t = t 1 + t 2 = v max α + v max β t = v max 1 α + 1 β = v max α + β αβ v max = t αβ α + β

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