Question

A $150\text{m}$ long train accelerates uniformly from rest. If the front of the train passes a railway worker $50\text{m}$ away from the station at a speed of $25\text{m/s}$, what will be the speed of the back part of the train as it passes the worker?

• A. $30\text{m/s}$
• B. $40\text{m/s}$
• C. $50\text{m/s}$
• D. $60\text{m/s}$

Answer 1

The correct option is C $50\text{m/s}$

Applying $3^{rd}$ equation of motion
$v^2=u^2+2as$
$25\times 25=0+2\times a\times 50$
$a=\frac{25}{4}{\text{m/s}}^2$
Now for speed of the back part of the train as it passes the worker
We have $v^{\prime 2}=v^2+2al$
where $l$ is the length of the train or distance covered by the back part to pass the worker
$v^{\prime 2}={25}^2+2\times \frac{25}{4}\times 150$
$v^{\prime 2}=625+(25\times 75)=2500$
$v^{\prime }=50\text{m/s}$