Kinematics Problem but not enough information?

[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' homework problems.
Anyway, to the problem:

Homework Statement

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

Homework Equations

kinematics equations

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!

 

[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.

 

[intriqet]

Thanks very much for the prompt reply but I am 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.

 

[rl.bhat]

Thanks very much for the prompt reply but I am 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.

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

 

[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?

 

[rl.bhat]

Your answers are correct.

 

[intriqet]

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

 

[rl.bhat]

bump

Have you entered delta T and deltaT1?

 

[intriqet]

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