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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 total time elapsed is \( t \), then maximum vellocity acquired by car will be
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(a) \( \frac{\left(\alpha^{2}-\beta^{2}\right) t}{\alpha \beta} \)
(b) \( \frac{\left(\alpha^{2}+\beta^{2}\right) t}{\alpha \beta} \)
(c) \( \frac{(\alpha+\beta) t}{\alpha \beta} \)
(d) \( \frac{\alpha \beta t}{\alpha+\beta} \)
(1994)
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