First slide
Instantaneous acceleration
Question

The relation between time and distance is t = αx2+βx, where α and β are constants. The retardation is

Difficult
Solution

dtdx = 2αx + β   v = 12αx+β

    a = dvdt = dvdx.dxdt

a = vdvdx = -v.2α(2αx+β)2 = -2α.v.v2 = -2αv3

  Retardation = 2αv3

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