# Commuter train

1. Nov 9, 2004

### miscellaneous

A commuter train can minimize the time t between two stations by accelerating (a1 = .20 m/s^2) for a time t1, then undergoing a negative acceleration (a2 = -.5 m/s^2) by using his brakes for a time t2. Since the stations are .90 km apart, the train never reaches its maximum velocity. Find the total travel time, t.

My method:

deltaS= (Vf^2-Vo^2)/2a
900= (Vf^2/.4) + (Vf^2)
900= 2.5Vf^2 + Vf^2
Vf= 16 m/s

and then I used: Vf = Vo + at
16= .2t
t=80 s

0= 16 - .5t
t=32 s

total t= 112 seconds

2. Nov 9, 2004

### Staff: Mentor

900 m is the entire distance. Note that the initial and final speeds are both zero over the 900 m.

Break the motion into two pieces, each with a different acceleration. Use that same kinematic formula, but for each piece separately. (The first piece goes from v = 0 to v = V1; the second goes from v = V1 to v = 0.)

3. Nov 9, 2004

### miscellaneous

I think that's what I did. Is my answer incorrect? I'm pretty sure my method is what you explained. If I'm wrong, please let me know. The Vf is the same as V1

4. Nov 9, 2004

### Staff: Mentor

Looks good. (I missed what you did, at first look.)

5. Nov 9, 2004

### miscellaneous

Ohh, thanks for the confirmation. I'm really happy I know what I'm doing