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Homework Statement
A subway train travels over a distance [itex] s [/itex] in [itex] t [/itex] seconds. it starts from rest and ends at rest. In the first part of its journey it moves with constant acceleration [itex] f [/itex] and in the second part with constant deceleration [itex] r \, [/itex].
Show that [itex] s \, = \, \frac {[\frac {fr} {f \, + \, r}] \, t^2} {2} [/itex]
Homework Equations
I know that [itex] s \,= \, (\frac {1}{2})(-r )t^2\, +\, v_it[/itex], where [itex] v_i \,=\, ft[/itex] but I'm not sure where to go from there. In particular, I can't figure out how to connect the seemingly separate equations for distance generated by the different accelerations into one function of time for the entire interval.
The Attempt at a Solution
By assuming that total acceleration is a sum of the given accelerations, I've gotten something that looks awfully close to the desired result, but am still not quite there:
[itex] s \,=\,\frac{1}{2} \,(f\,+\,r)\,t^2 \, + \,v_i\,t [/itex]
I feel like I'm missing something.
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