Confusion with train collision with constant acceleration

[Petterandre]

The problem statement
A train starts out from Stavanger at 8.14, in direction of Kristiansand. It goes with constant speed, 80.0km/h until Sandnes,
a distance of 15.0 km. Then it accelerates (instantaneously) to 120 km/h and proceeds towards Kristiansand. Kristiansand is
250 km from Stavanger.

A second train starts out from Kristiansand at 9.28, direction Stavanger. The driver immediately falls asleep with his foot
on the accelerator, and the train accelerates at a constant rate of 0.100 m/s^2, until it reaches the maximum speed of 160
km&h. It then accelerates no longer, but continues towards Stavanger at that maximum speed.

b) at what time, and at which distance from Kristiansand does the second train reach the maximum speed?
c) Where is the first train, when the second train reaches maximum speed?
d) Where, when and at what relative speed do the two trains collide.

My attempt at a solution


http://puu.sh/blx4Q/596557edba.jpg


a) was simple. Just when the first train arrives at Sandnes.


However, I continued on with b) and c), using this formula

v = vo + at

This just doesn't seem right though!
Is it just my mind playing tricks on me, or is 7,41 minutes (444,45sec) too fast to reach 160km/h?


Anyhow, if this is actually correct, I am struggling with the d) question. I just don't know how to set this up.
If both trains had a standard speed, it would be simple, but since we are talking acceleration, I find it hard.

I was thinking of perhaps taking the distance traveled when the 2nd train hits 160km/h and just use this to calculate
the average speed over the entire 250km travel, so I would have to say distance 1 (from standstill to 160km/h) +
distance 2 (from 160km/h until we got to Stavanger)


Basically, I'm not sure which formulas to use. I thought it was the one I used, but I'm a little scared to go with it, since
I'm not sure if I trust my results.

If any of you could take a look at this, I would be very thankful!

 

[haruspex]

Your answer to b is correct.
For d, it might be easier to take the frame of reference of the constant speed train, so you just have one object with constant acceleration and a known distance to cover.