d
(d) Let the car accelerate at rate \(\alpha \) for time \({t_1}\) then maximum velocity attained, \(v = 0 + \alpha {t_1} = \alpha {t_1}\)

Now, the car decelerates at a rate \(\beta \) for time \((t - {t_1})\) and finally comes to rest. Then,

\(0 = v - \beta (t - {t_1})\) \(⇒\) \(0 = \alpha {t_1} - \beta t + \beta {t_1}\)

\(⇒\)  \({t_1} = \frac{\beta }{{\alpha + \beta }}t\)

 \(v = \frac{{\alpha \beta }}{{\alpha + \beta }}t\)