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A student is running to catch a bus. When the student is 40m away, the bus begins accelerating from rest with a constant acceleration of .170m/s^2. What is the minimum speed she must run to catch the bus?

This is what I've done so far:

[tex]x_{bus}=1/2*.17*t^2[/tex]

[tex]x_{girl}=-40+v_0t[/tex]

[tex]1/2*.17*t^2=-40+v_0t[/tex]

[tex]v_0=.085t+40/t[/tex]

And this is where I get stuck. I'm having a hell of a time getting rid of that unknown time. I've tried integrating that and setting it equal to the position of the bus but nothing is matching up with the correct answer in the back of the book. Any ideas?