Question

# The relation between time t and distance x is t=αx2+βx where α  and β are constants. The retardation is2 βv32 αβv32 β2v32 αv3

Solution

## The correct option is D 2 αv3Given 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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