First slide
Instantaneous acceleration
Question

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

Moderate
Solution

dtdx=1V=2αx+β
or V=12αx+β
a=dvdt=dvdxdxdt=vdvdx=v2a(2αx+β)2=2αv3
So, Retardation =2αv3 

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