Question

A train is travelling towards the station on a straight track. It is a certain distance from the station when the engineer applies the brakes. Initially, the train is moving at 50 m/s and slows down at 2.5 m/s^2. If the train stops at the station, how far before the station did the engineer apply the brake?

Answer 1

500 m

Step-by-step explanation:

t = Time taken

u = Initial velocity = 50 m/s

v = Final velocity = 0

s = Displacement

a = Acceleration = -2.5 m/s²

Equation of motion

`v=u+at\\\Rightarrow 0=50-2.5* t\\\Rightarrow (-50)/(-2.5)=t\\\Rightarrow t=20\ s`

Time taken by the train to stop is 20 seconds

`s=ut+(1)/(2)at^2\\\Rightarrow s=50* 20+(1)/(2)* -2.5* 20^2\\\Rightarrow s=500\ m`

∴ The engineer applied the brakes 500 m from the station