Question

A car starts from rest and travels with uniform acceleration $\alpha$ for some time and then With uniform retardation $\beta$ and comes to rest If the total time of travel of the car is 't' the maximum velocity attained by it is given by

• A. $\frac{\alpha \beta}{(\alpha+\beta)} t$
• B. $\frac{1}{2}\frac{\alpha \beta}{(\alpha+\beta)} t^2$
• C. $\frac{\alpha \beta}{(\alpha-\beta)} t$
• D. $\frac{1}{2}\frac{\alpha \beta}{(\alpha-\beta)} t^2$

Answer 1

Answer: (A)

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

Answer 2

maximum velocity $\nu = \alpha t_1 = \beta t_2$ and $t = t_1 + t_2$ $\Rightarrow \, \frac{\nu}{\alpha} + \frac{\nu}{\beta} = t = \Rightarrow \nu = \frac{(\alpha \beta)t}{(\alpha + \beta)}$ S = $ut + \frac{1}{2} at^2$