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A car starts from rest and travels with uniform acceleration ‘α’, for some time and then with uniform retardation ‘β’ and comes to rest. The time of motion is “t”. Find the maximum velocity attained by it. (αβt/(α+β))

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Acceleration a = a m/sec2 

Initial speed u = 0 m/sec

 Let the time be t1 sec. 

From equation v = u + at 

⇒ v = 0 + αt1

Retardation a = – β m/sec2 

Initial speed ‘u’ is equal to the final velocity with acceleration ‘α’ 

= u = αt1 m/sec 

Final velocity v = 0 m/sec 

Let the time be t2 sec

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