Physics

I'm trying to prep for an exam, but I am struggling with the practice questions. I have answers for both questions, but I'm 95% sure they are incorrect.

1. Two students decide to run a race. The first student starts off at a constant speed of 5 m/s while the second student isn't paying attention. Two seconds later that student takes off from rest and accelerates at 0.5 m/s^2. At what time will the two runners meet again?

My work:
I used the equation v= v0 + at

5 = 0.5 + (-9.8)(t)
4.5 = -9.8t
t= -0.4591...
+ 2 s = 1.54 s, but I don't think this is correct because I came up with a -t, which is impossible. If I take the negative sign away from 9.8, I get 2. 46 s, but a= -9.8 it is a gravitational constant, so I can't do that.

2. A dart is thrown horizontally toward the bull's eye on the dart board, with an initial speed of 9.50 m/s. It hits a point on the rim vertically below 0.17 s later. What is the distance below the rim the dart strikes?

My work: I used equation delta y= Vot + 0.5(at^2)

y= (9.5)(0.17) + 0.5(-9.8)(0.17)^2
y= 1.615 - 0.14161
y= 1.75661 m

Please Help!

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  1. 1. Two students decide to run a race. The first student starts off at a constant speed of 5 m/s while the second student isn't paying attention. Two seconds later that student takes off from rest and accelerates at 0.5 m/s^2. At what time will the two runners meet again?
    -----------------------------------
    The point is that they go the same distance but the first runner runs 2 seconds longer
    d = 5 (t+2)
    for the second runner
    d = 0 + 0 t + (1/2)(.5) t^2
    so
    5 t + 10 = .25 t^2
    t^2 -20 t - 40 = 0
    t = [ 20 +/-sqrt(400+160)]/2
    t = [ 20 +/- 23.67 ]/2
    t = 21.8
    so the second runner runs for 21.8 and the first runner runs for 23.8 seconds

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