Question

Question: The relation between time and distance is t = α x 2 + β x , where α and β are constants. The retardation is ??in this question I am clear until v = 1/(2.alpha.x +beta) but I am not able to differentiate the velocity to get acceleration.i.e I want step by step procedure of the differentiation with reasons after each step

Answer 1

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