Calculating Time for Subway Travel with Maximum Acceleration

[jehan4141]

You can find this problem with supplemental pics on page 6 at http://www.physics.princeton.edu/~mcdonald/examples/ph101_2006/learning_guide_ph101_2006.pdf

Suppose that the maximum possible acceleration for passengers standing on a subway is 0.1 m/s^2 and that two subway stations are 0.7 km apart.

What is the minimum possible time taken between the two subways stations?
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The answer is 170 seconds. I keep getting 118 seconds :(

My calculations are as follows:

x = (0.5)(acceleration)(time^2) where x = 700 meters and acceleration is 0.1

thus, sqrt(2x/acceleration) = time = 118

Can anybody tell me what I am doing wrong?

 

[Pi-Bond]

I think the train has to stop at both stations, so you need to impose the condition that the velocity at both stations is zero. Right now the velocity won't be zero at the next station.

 

[Doc Al]

Can anybody tell me what I am doing wrong?

What must the speed be at the start and end of the trip?

 

[daveb]

They may be thinking that you accelerate fo half the distance, then decelerate for the remaining half.

 

[jehan4141]

Yes! Thank you so much everyone!