A pedestrian is running at his maximum speed of 6.0m/s to catch a bus stopped by a traffic light. When he is 25m away from the bus the light changes and the bus accelerates uniformly at 1.0m/s^2. Find either (a) how far he has to run to catch the bus or (b) his frustration distance(closest approach)

Answer 1

a. d2 = d1 - 25,
6t = 0 + 0.5 * 1t^2 - 25,
6t - 0.5t^2 + 25 = 0,
-0.5t^2 + 6t + 25 = 0,
Use Quadratic Formula to find t:
t = 15.27s.

d = Vt = 6 * 15.27 = 91.6m.

Answer 2

10m