Question

A train is traveling down a straight track at 27 m/s when the engineer applies the brakes, resulting in an acceleration of −1.0 m/s2 as long as the train is in motion. How far does the train move during a 54-s time interval starting at the instant the brakes are applied?

Answer 1

Answer:

364.5 m

Explanation:

Initial speed = u = 27 m/s

Acceleration = a = -1 m/s²

Distance = s

$v^2-u^2=2as\\\Rightarrow 0-27^2=2\times -1s\\\Rightarrow \frac{729}{2}=s\\\Rightarrow s=364.5\ m$

Time taken = t

$v=u+at\\\Rightarrow t=\frac{v-u}{a}\\\Rightarrow t=\frac{0-27}{-1}\\\Rightarrow t=27\ s$

So, in 27 seconds the train will stop and will have travelled a distance of 364.5 m.

So, the rest of the 27 seconds it will not move.

Hence, the distance covered in 54 seconds will be 364.5 m.