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.

 t = ax2 + 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 = -2av3

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