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