• # question_answer A person is at a distance x from a bus when the bus begins 10 move with a constant acceleration a. What is the minimum velocity with which [he person should run towards the bus so as to catch it? A)  $2ax$                                 B)  $\sqrt{2ax}$ C)  $ax$                   D)         $\sqrt{ax}$

Let the person catches 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,                                 ${{b}^{2}}-4ac\ge 0$ ${{(-2v)}^{2}}-4\times a\times 2x\ge 0$ $4{{v}^{2}}-8ax\ge 0$ ${{v}^{2}}-2ax\ge 0$ ${{v}_{\min }}=\sqrt{2ax}$