# Kinematics Problem but not enough information?

1. Sep 22, 2009

### intriqet

Hi Guys, its my first post here and I have a feeling that I'll be using this forum as a resource. Maybe once I learn enough I'll be able to contribute in solving other peoples' hw problems.
Anyway, to the problem:

1. The problem statement, all variables and given/known data

A commuter train travels between two downtown stations. Because the stations are only 1.42 km apart, the train never reaches its maximum possible cruising speed. During rush hour the engineer minimizes the travel interval deltaT between the two stations by accelerating for a time interval deltaT1 at a1 = .100m/s^2 and then immediately braking with acceleration a2 = -.390 m/s^2 for a time interval deltaT2. Find the minimum time interval of travel deltaT and the time interval deltaT1.

So we are given:
A1 = .1 m/s^2 A2 = -.390 m/s^2
V i1 = 0 m/s Vf2=0m/s
delta X = 1420 m

2. Relevant equations

kinematics equations

3. The attempt at a solution

I feel like I'm overthinking this one and am overlooking a relatively simple solution. I know can't use 1420 as deltaX because the train does not accelerate at one rate for the entire distance. Now I only have 2 variables for the first half of the problem.

Please any hints will greatly help asap. Thanks!

2. Sep 22, 2009

### rl.bhat

In the first half, vf = a1T1, in the second half vi = a2T2.
vf = vi = v.
Hence a1T1 = a2 T2. Find T1
Next x1 = 0.5*a1*T1^2....(1)
x2 = 0.5*a2*T2^2....(2)
Sustitute the value of T1 in eq.(1) and add it to eq.(2). (x1 + x2) is know. Find T2.

3. Sep 22, 2009

### intriqet

Thanks very much for the prompt reply but Im not quite sure I understand.

Based on your hint, I plugged in a1T1 for Vf in Vf^2-Vi^2 = 2AxDeltaX. leaving me with T1 = sqrt(2DeltaX).

Please tell me if I'm going the correct direction and please excuse the fact that I'm a complete DA.

4. Sep 22, 2009

### rl.bhat

You have to find T1 as
T1 = a2*T2/a1.Put it in equation (1)

5. Sep 22, 2009

### intriqet

Thanks to your help I was able to derive some answers! The answer I got for t2 is 50.1 s and t1 195 s. So the entire trip was 245 s long. Is this correct?

6. Sep 22, 2009

### rl.bhat

7. Sep 22, 2009

### intriqet

Blurg! Webassign will not take my answers. Any other suggestions?

8. Sep 23, 2009

### rl.bhat

Have you entered delta T and deltaT1?

9. Sep 23, 2009

### intriqet

Yessiree. I think it's webassign but I guess I can skip this problem it's for extra credit.