. A train is traveling down a straight track at 20 m/s when the engineer applies the brakes,

Question

resulting in an acceleration of -1.0 m/s
2
as long as the train is in motion. How far does the
train move during a 40-s time interval starting at the instant the brakes is applied?

Answer 1

v =Vi + a t = 20 -1.0 t
the train moves forward until v = 0, then backward
How far it moves includes both directions
Lets do eastward
0 = 20 - 1.0 t
t = 20 seconds to stop
x = Xi + Vi t - (1/2) a t^2
x = 0 + 20(20) - 0.5 (20)^2
x = 200 meters
now it does backwards, you can just say back 200 meters due to the symmetry
so 200 forward and 200 backward = 400 meters total
by the way the average speed during each phase is (20+0)/2 = 10 m/s
so you could have just said 10 * 20 = 200 meters each way