A) \[\frac{\alpha \beta }{\alpha +\beta }t\]
B) \[\frac{\alpha \beta }{\alpha -\beta }t\]
C) \[\sqrt{\alpha \beta }\,t\]
D) \[\frac{\alpha +\beta }{2}t\]
Correct Answer: A
Solution :
Let \[{{v}_{0}}\] be the maximum velocity, then Case I \[u=0,\,\,v={{v}_{0}},\,\,a=\alpha ,\,\,t={{t}_{1}}\] (say) Using, \[v=u+at\Rightarrow \,{{v}_{0}}=\alpha {{t}_{1}}\Rightarrow \,{{t}_{1}}=\frac{{{v}_{0}}}{\alpha }\] ?(i) Case II \[u={{v}_{0}},\,\,v=0,\,\,a=-\beta ,\,\,t={{t}_{2}}\] (say) Using \[v=u+at\,\,\,\Rightarrow \,\,\,0={{v}_{0}}-\beta {{t}_{2}}\] \[\Rightarrow \] \[{{t}_{2}}=\frac{{{v}_{0}}}{\beta }\] But \[{{t}_{1}}+{{t}_{2}}=t\] \[\frac{{{v}_{0}}}{\alpha }+\frac{{{v}_{0}}}{\beta }=t,\] \[{{v}_{0}}=\frac{\alpha \beta }{\alpha +\beta }t\]
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