Question

A person is at a distance $x$ from a bus when the bus begins to move with a constant acceleration $a$ .What is the minimum velocity with which the person should run towards the bus so as to catch it ?

• A. $2ax$
• B. $\sqrt{2ax}$
• C. $ax$
• D. $\sqrt{ax}$

Answer 1

The correct option is B $\sqrt{2ax}$

Let the person catches the bus in $t$ second.
Distance covered by bus , $s=\frac{1}{2}a{t}^2$
Distance covered by person =$vt$
According to condition,
$s+x=vt$
$\frac{1}{2}a{t}^2+x=vt$
$a{t}^2+2x=2vt$
$a{t}^2-2vt+2x=0$
For $t$ to be real,
$b^2-4ac\ge 0$
$(-2v{)}^2-4\times a\times 2x\ge 0$
$4v^2-8ax\ge 0$
$v^2-2ax\ge 0$
$v_{min}=\sqrt{2ax}$