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 A car accelerates from rest at a constant rate alpha for some time after which it decelerates at a constant rate
beta and comes to rest. if the total time elapsed is 't' then prove that maximum velocity acquired by the car is
                                                          alpha betat
                                    =               long dash long dash long dash long dash      
                                                         (alpha plus beta   )    

Asked by Hrishikesh marathe 13th June 2016, 7:30 AM
Answered by Expert
Answer:
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.
 
begin mathsize 12px style straight alpha equals straight v over straight t subscript 1 space or space straight t subscript 1 equals straight v over straight alpha space....... space left parenthesis Equation space 1 right parenthesis end style
 
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.

begin mathsize 12px style straight beta equals fraction numerator straight v over denominator straight t minus straight t subscript 1 end fraction space or space straight t minus straight t subscript 1 equals straight v over straight beta space........ space left parenthesis Eqaution space 2 right parenthesis
adding space equation space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space we space get
straight t equals straight v open parentheses 1 over straight alpha plus 1 over straight beta close parentheses
rightwards arrow straight v equals open parentheses fraction numerator straight alpha space straight beta over denominator straight alpha plus straight beta end fraction close parentheses straight t end style

Answered by Expert 13th June 2016, 1:04 PM
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