Question

Two particles start moving from the same point along the same straight line. The first moves
with constant velocity 'u' and the second with constant acceleration 'a'. During the time that
elapses before the second catches the first, the greatest distance between the particles is​

Answer 1

Explanation:

Difference between particle 1 and 2 at time t is given by

$d = ut - \frac{1}{2} a {t}^{2}$

for maxima let it derivative = 0

$u - 2at = 0 \\ t = \frac{u}{2a}$

and distance will be

$d = \frac{ {u}^{2} }{2a} - \frac{a. {u}^{2} }{8 {a}^{2} } = \frac{3 {u}^{2} }{8a}$