Question

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

• A. $\frac{v^2}{a}$
• B. $\frac{v^2}{2a}$
• C. $\frac{2v^2}{a}$
• D. $\frac{v^2}{4a}$

Answer 1

Answer: (B)

Let $x$ be the distance between the particles after $t$ seconds. Then
$ x = vt - \frac{1}{2} at^2 \,\,....(1)$
For $x$ to be maximum
$\frac{dx}{dt} = 0$
or $v - at = 0$
or $t = \frac{v}{a}$
substituting this value in $(1)$ we get
$x = v(\frac{v}{a}) -\frac{1}{2} a(\frac{v}{a})^2$
or $ x = \frac{v^2}{2a}$