Locomotive Time?

Question

A locomotive is accelerating at 1.6 m/s2. It passes through a 18.0 m wide crossing in a time of 2.4 s. After the locomotive leaves the crossing, how much time is required until its speed reaches 27 m/s?

I tried this many times, different ways. I thought the answer was 12.1875s, but I guess I was wrong. If anyone would help me solve this, Id really appreciate it

Answer 1

First of all, we don't know the length of the locomotive, so I will assume that the locomotive is a point mass.

From what is given in the problem and using
d=d0+v0*t+.5*a*t^2
we can write
18.0=0+v0*2.4+.5*1.6*2.4^2
where v0 is the speed the locomotive at the entrance to the crossing.
Solve for v0
v0=5.58 m/s

The t' to get to 27 m/s after exiting the crossing related to
v=v0+a*(t'+2.4)
plugging in the numbers
27=5.58+1.6*(t'+2.4)
solve for t'
t'=10.99 seconds

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