The relation between time t and distance x is ax^2+bx, where a,b are constants. the retardation is _____.

I think the correct equation would be t = ax^{2}+bx. Please let me know if this wrong.

So, if t = ax^{2}+bx

then, 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}

Hence, retardation= 2av^{3}