Question

The distance between 2 stations is 2 km. A train covers it in 1 minute. It accelerates and retards at the same rate of 0.2m/s². What is the maximum velocity attained by the train?: The distance between 2 stations is 2 km. A train covers it in 1 minute. It accelerates and retards at the same rate of 0.2m/s². What is the maximum velocity attained by the train?

Answer 1

Lets us find out the equation of maximum velocity when a train first accelerates with $\alpha \space m/sec^2$

and then retards with $\beta \space m/sec^2$ with total time being $t$ .

for acceleration time $t_1$ :

$v=u+at_1$

This v will be $v_{max}=\alpha t_1$ .......(1) as u=0

For retardation time t₂:

$v=u+at \implies 0=\alpha t_1-\beta t_2$ (as final velocity is zero)

$\alpha t_1=\beta t_2 \implies t_2=\frac{ \alpha}{ \beta}\times t_1$

Total time=$t=t_1+t_2\implies t_1+\frac{ \alpha}{ \beta}\times t_1=t$

$t_1=\frac{\beta t}{\alpha +\beta}$.......(2)

Using (1) and (2)

$v_{max}=\frac{\alpha \beta t}{\alpha +\beta}$

In this question $\alpha ,\beta$ and $t$ are 0.2$m/sec^2$ ,0.2$m/sec^2$ and 60 sec(1 min=60 sec) respectively.

$v_{max}=\frac{0.2\times0.2\times60}{0.2+0 .2}=6m/sec$