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

• A

  $\left(\frac{{\alpha }^2-{\beta }^2}{\alpha \beta }\right)t$
• B

  $\left(\frac{{\alpha }^2+{\beta }^2}{\alpha \beta }\right)t$
• C

  $\frac{(\alpha +\beta )t}{\alpha \beta }$
• Correct answer
  D

  $\frac{\alpha \beta t}{\alpha +\beta }$

Hence, the correct answer is option: 'D'.