Let there be $2$ objects $P_1$(initial velocity $u$ $ms^{-1}$ & acceleration $a$ $ms^{-2}$) & $P_2$ (initial velocity $U$ $ms^{-1}$ & acceleration $A$ $ms^{-2}$) initially separated by distance of $x_0$ metre.
Relative displacement, $D$ at time $t$ is given by $$D(t)=x_0+Ut+\frac{At^2}{2} - ut - \frac{at^2}{2}$$
If we differentiate them wrt time then we get $$\frac{d}{dt}D(t)=U + At - u - at$$
When $\frac{d}{dt}D(t)=0$, then either the distance between them is maximum or minimum. And we get
$$U + At - u - at = 0$$ $$\implies U + At = u + at$$
My book says that
IN MOST OF THE CASES at minimum distance, $v_1 = v_2$.
What I wrote above was my derivation of that statement. But I think this value can correspond to the maxima also. So why is it that we are considering it the minimum value?
Please explain.
Thanks:)
