Posted by Raf on Tuesday, October 18, 2011 at 2:51pm.
1. Carlos jogs in a straight line at a constant speed of 1.5 m/s. He passes by Victoria, who, 10 seconds after Carlos had passed her, starts accelerating at a constant rate of 0.50 m/s^2
a) How much time after the passing of Carlos does it take Victoria to catch up to him?
b) What distance did they travel?

Physicss  Steve, Tuesday, October 18, 2011 at 3:31pm
Assuming that Victoria was standing still when Carlos passed her, we have the following equations, calling t=0 when he passes her:
Carlos: s = 1.5t
Victoria: s = .25(t10)^2
set them equal to find when they have traveled the same distance  that is, when she passes him.
1.5t = .25(t^2  20t + 100)
1.5t = t^2/4  5t + 25
t^2/4  6.5t + 25 = 0
t^2  26t + 100 = 0
t = 13 ± √69
t = 4.7, 21.3
Since Victoria does not start till t=10, the only answer is 21.3, or 11.3 seconds after she started running.
Plug in times to get distances.
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