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

364.5 m

Step-by-step explanation:

Initial speed = u = 27 m/s

Acceleration = a = -1 m/s²

Distance = s

`v^2-u^2=2as\\\Rightarrow 0-27^2=2* -1s\\\Rightarrow (729)/(2)=s\\\Rightarrow s=364.5\ m`

Time taken = t

`v=u+at\\\Rightarrow t=(v-u)/(a)\\\Rightarrow t=(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.