Assume that the brakes in your car create a constantdeceleration, regardless of

Question

Assume that the brakes in your car create a constantdeceleration, regardless of how fast you are going. if you doubleyour driving speed, how does this affect the time required to cometo a stop and the distance needed to stop? Answer is time will be doubled and distance needed to stopwill be multiplied by a factor of four I dont understand why mainly the second part. Pleaseexplain. Assume that the brakes in your car create a constantdeceleration, regardless of how fast you are going. if you doubleyour driving speed, how does this affect the time required to cometo a stop and the distance needed to stop? Answer is time will be doubled and distance needed to stopwill be multiplied by a factor of four I dont understand why mainly the second part. Pleaseexplain.

Explanation / Answer

Let Accleration be  - a Initial speed of the car u = v Final speed v = 0 time taken to stop t = ( v - u ) / a                               = v / a After increases the speed from v to 2v time t ' = ( 0 - 2v ) / - a          = 2t Distance moved   S = ut + ( 1/ 2 ) at^2                       Or S = vt - ( 1/ 2) at^2                             S = -( 1/ 2) ( -a ) t ^ 2                                = ( 1/ 2) a t ^ 2          Or ( S' / S ) = ( t ' / t ) ^ 2                               = ( 2t / t ) ^ 2                                = 4                              S ' = 4 S                               

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