A) \[2ax\]
B) \[\sqrt{2ax}\]
C) \[ax\]
D) \[\sqrt{ax}\]
Correct Answer: B
Solution :
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, \[{{b}^{2}}-4ac\ge 0\] \[{{(-2v)}^{2}}-4\times a\times 2x\ge 0\] \[4{{v}^{2}}-8ax\ge 0\] \[{{v}^{2}}-2ax\ge 0\] \[{{v}_{\min }}=\sqrt{2ax}\]
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