Q13 of 24 Page 31

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.

Given, initial velocity = 0, acceleration = α and retardation = β


Let the time of accelerated motion be t’ and time of retarded motion be t”, so that t’ + t” = t … (1)


Velocity after time t’, v1 = 0 + αt’ (using v = u + at) …(2)


Now, v1 will be initial velocity for retarded motion and


final velocity = 0 and acceleration


0 = v1- βt” …(using v = u + at)


Or, …(3)


Now, in equation (2)









As, after time t’ , retardation will start so maximum velocity will


be at time t’ which is v1 .


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