A car accelerates from rest at a constant rate \[\alpha \]for some time, after which it decelerates at a constant rate \[\beta \]and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is [IIT 1978; CBSE PMT 1994]

• 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.               \[\frac{\alpha \beta \,t}{\alpha +\beta }\]