A car accelerates from rest at a constant rate α for some time

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 prove that maximum velocity acquired by the car is

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From rest, the car accelerates for a timr t1.

Thus, its velocity-time graph is a staright line OA sloping in the upward direction.the maximum velocity of the car be considered to be ‘v’.

The slope of the graph OA gives the accelration of the car.
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The car begins decelerate after attaining the maximum velocity.Thus, its velocity-time graph is a straight line AB sloping in th edownward direction.The slope of the graph AB gives the detardation of the car.
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