A) \[\frac{{{\text{v}}^{2}}}{a}\]
B) \[\frac{{{v}^{2}}}{2a}\]
C) \[\frac{\text{2}{{\text{v}}^{2}}}{a}\]
D) \[\frac{{{\text{v}}^{2}}}{4a}\]
Correct Answer: B
Solution :
Initial relative velocity, \[{{\text{v}}_{\text{AB}}}\text{=v}-0=\text{v}\text{.}\] Acceleration \[{{\text{a}}_{\text{AB}}}=\text{ }0-\text{a=a}\] For max. Separation \[{{\text{v}}_{\text{AB}}}=0\] \[\text{0=}{{\text{v}}^{\text{2}}}-\text{2as}\Rightarrow \text{s=}\frac{{{\text{v}}^{\text{2}}}}{\text{2a}}\]
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