The relation between time(t) and distance(x) is t=Ax^2 + Bx, A and B are constants. Prove that its retardation is 2Av^3.

^{2} + bx

=> Differentiate both side with respect to time (t)

=> dt/dt = 2ax.dx/dt + b.dx/dt

=> 1 = 2axv + bv

=> v.(2ax + b) = 1

=> (2ax + b) = 1/v

=> Again differentiate both side with respect to time (t)

=> 2a.dx/dt = -v^{-2} . dv/dt

=> 2av = v^{-2} . acceleration

=> acceleration = -2av^{3}

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