# When will velocities of the trains equal?

1. Sep 30, 2015

### Entr0py

1. The problem statement, all variables and given/known data
A train having a velocity of x m/s is caught by a train accelerating from zero 20 seconds after the second train starts. At what time were their velocities equal?

2. Relevant equations

3. The attempt at a solution
I was thinking that you'd have to assume that the train with x velocity is traveling with constant velocity and that the second train starts at t=t-20 s. However, I'm confused as to how I would find when their velocities would be equal.

2. Sep 30, 2015

### Bystander

How far does the first train travel?

3. Sep 30, 2015

### Entr0py

So in 20 s, the first train has traveled x=x0+v0t+.5at^2. well I assumed it started from rest, so x=.5a(400) or 200a m.

4. Oct 1, 2015

### Bystander

I'd call that the second train from my reading of the problem statement. Let's tidy up the statement a bit so we're both discussing the same trains. "Train A is moving at a constant velocity of x m/s. As it pulls even with Train B, Train B accelerates from 0 at a constant rate, and pulls even with A after 20 seconds. At what time are the two velocities equal?"

Now, I ask how far does Train A travel?

5. Oct 1, 2015

### Entr0py

I'm sorry I'm confused?

6. Oct 1, 2015

### haruspex

You need to say exactly what is confusing you. Bystander's description of the problem is correct. I'll try to make it more concrete.
At t=0, both trains are at s=0. Train A is moving at constant speed x, train B is stationary.
Train B then accelerates at some unknown constant (we must assume) rate a. At t=20, the trains have travelled the same distance. Train B must now be moving faster than train A.
At what time was train B moving at speed x?

Bystander is asking you, first, how far train A travelled in those 20 seconds.