Question

A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is $t$, the maximum velocity acquired by the car is given by

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

Answer 1

The correct option is D $\left(\frac{\alpha \beta }{\alpha +\beta }\right)t$

Let maximum velocity=$v$

Now,$v=0+\alpha t_1$

Similarly,$0=v-\beta t_2$

From the above equations we get, $t_1=\frac{v}{\alpha }\&t_2=\frac{v}{\beta }{t}_1+t_2=t=\frac{v}{\alpha }+\frac{v}{\beta }\Rightarrow v=\frac{\alpha \beta }{\alpha +\beta }t$