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Question

The relation between time t and distance x is t=αx2+βx where α  and β are constants. The retardation is
  1. 2 βv3
  2. 2 αβv3
  3. 2 β2v3
  4. 2 αv3


Solution

The correct option is D 2 αv3
Given t=αx2+βx
Differenting w.r.t time, we get 1=2αdxdt.x+βdxdt v=dxdt=1β+2αx
Differentiating one more time w.r.t  t, we get d2xdt2=(β+2αx).ddt(1)1.ddt(β+2αx)(β+2αx)2
         =2αv(β+2αx)2=2αv3
Negative sign represents retardation.

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