A locomotive is accelerating at 1.60 m/s2. It passes through a 20.0-m-wide crossing in a time of 2.40 s. After the locomotive leaves the crossing, how much time is required until its speed reaches 31.6 m/s

The time to reach 31.6 m/s is 14.54 s.

Explanation:

Given;

acceleration of the locomotive, a = 1.60 m/s²

distance traveled by the locomotive, s = 20 m

time of motion, t = 2.4 s

final velocity of the locomotive, v = 31.6 m/s

The speed of the of the locomotive as it leaves the 20 m wide crossing;

The time to reach 31.6 m/s is calculated from the equation below;

v = u + at

31.6 = 8.333 + 1.6t

1.6t = 31.6 - 8.333

1.6t = 23.267

t =  23.267 / 1.6

t = 14.54 s

Therefore, the time to reach 31.6 m/s is 14.54 s.