A body starting from rest, accelerates at a constant rate \( a \mathrm{~m} / \mathrm{s}^{2} \) f...

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A body starting from rest, accelerates at a constant rate \( a \mathrm{~m} / \mathrm{s}^{2} \) for some time after which it decelerates at a constant rate \( \mathrm{b} \mathrm{m} / \mathrm{s}^{2} \) to come to rest finally. If the total time elapsed is \( t \mathrm{sec} \), the maximum velocity attained by the body is given by
[AMU PMT 2009]
(a) \( \frac{a b}{a+b} t \mathrm{~m} / \mathrm{s} \)
(b) \( \frac{a b}{a-b} \mathrm{tm} / \mathrm{s} \)
(c) \( \frac{2 a b}{a+b} t \mathrm{~m} / \mathrm{s} \)
(d) \( \frac{2 a b}{a-b} \mathrm{tm} / \mathrm{s} \)
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