# Maximum acceleration homework

## Homework Statement

If the maximum acceleration that is tolerable for passengers in a subway is 1.70 m/s2, and the subway stations are located 699 m apart, what is the maximum speed that the train attains between stations?

## Homework Equations

d= v(initial)t + .5at^2

## The Attempt at a Solution

699m = 0t + .5(1.7)t^2

Is this wrong, I don't know what to do. thanks

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kuruman
Homework Helper
Gold Member

First off, you are not calculating a speed. You are calculating how long it will take the train to reach the next station if it were accelerating all the way.

You need to consider that the train will have to accelerate at the maximum acceleration for half the distance and then decelerate at the same maximum but opposite acceleration for the other half of the distance so that it is at rest when it reaches the next station. The maximum speed that problem is asking is attained at the half-way point.

so I would want to solve for t right? The time it will take? also should i cut the distance (d) in half to 349.5? Sorry, I'm just not very good at this but thank you very much for any help.

rl.bhat
Homework Helper

First off, you are not calculating a speed. You are calculating how long it will take the train to reach the next station if it were accelerating all the way.

You need to consider that the train will have to accelerate at the maximum acceleration for half the distance and then decelerate at the same maximum but opposite acceleration for the other half of the distance so that it is at rest when it reaches the next station. The maximum speed that problem is asking is attained at the half-way point.
It is also possible that the train attains maximum speed with maximum acceleration, moves certain distance and then again slows down with maximum retardation before coming stop.

kuruman