question_answer

A car accelerates from rest at a constant rate a for some time, after which it deaccelerates at a constant rate j3 and comes to rest. If the total time elapsed is (, 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) \[\frac{(\alpha +\beta )}{\alpha \beta }t\]                  

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

Correct Answer: D

Solution :

[d] From the figure we have, MP \[={{v}_{\max }}=\alpha \,{{t}_{1}}=\beta \,{{t}_{2}}\] But \[t={{t}_{1}}+{{t}_{2}}\] \[={{v}_{\max }}\left( \frac{1}{\alpha }+\frac{1}{\beta } \right)\] \[={{v}_{\max }}\left( \frac{\alpha +\beta }{\alpha \beta } \right)\] \[\therefore \,\,\,{{v}_{\max }}=\frac{\alpha \beta t}{\alpha +\beta }\] So, the correct answer is [d].