question_answer

A car accelerates from rest at a constant rate a for some time, after which it decelerates at a constant rate \[\beta \] and comes to rest. to the total time elapsed is t, then the maximum velocity acquired by the car is-

A) \[\left( \frac{{{\alpha }^{2}}+{{\beta }^{2}}}{\alpha \beta } \right)t\]               

B) \[\left( \frac{{{\alpha }^{2}}-{{\beta }^{2}}}{\alpha \beta } \right)t\]

C) \[\frac{(\alpha -\beta )t}{\alpha \beta }\]              

D) \[\frac{\alpha \beta t}{\alpha +\beta }\]

Correct Answer: D

Solution :

\[t={{t}_{2}}+{{t}_{2}}\] \[\alpha =\frac{{{V}_{\max }}}{t}\] \[\beta =\frac{{{V}_{\max }}}{{{t}_{2}}}\]             \[\therefore \,\,\,t=\frac{{{V}_{\max }}}{\alpha }+\frac{{{V}_{\max }}}{\beta }\] \[\therefore \,\,\,{{V}_{\max }}=\frac{t\alpha \beta }{\alpha +\beta }\]