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A commuter train travels between two downtown stations. Because the stations are only 1.00km apart, the train never reaches its maxium possible cruising speed. The engineer minimizes the time t between the two stations by accelerationg at a rate a1=0.100m/s^2 for a time t1 and then by breaking with acceleartion a2=-0.500m/s^2 for a time t2. Find the minimum time of travel t and the time t1.

hmmm, not sure where to begin. I ws thinking about finding the distance first, then relate it to time. I tried to set the distance of t1 to the distance of t2, something on the lines of:

Vi^2=2ad-Vf^2...Vi would be 0 since the train starts at zero m/s

Vf^2=2ad-Vi^2...Vf would be 0 since the train will make a complete stop

so...2ad-Vf^2=2ad-Vi^2

however, that wouldn't work because the distances are not the same

Any suggestions?

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# Homework Help: Acceleration and deceleration

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