Uniform accelerated motion (UAM) equations, a.k.a. "kinematics equations":
For constant speed:
Δx = ct
xfinal - xinitial = ct
xfinal = xinitial + ct
xfinal = xman
Assuming the bus is moving in a positive direction, xinitial = -b
A man is running at speed c (much less than the speed of light) to catch a bus already at a stop. At t = 0, when he is a distance b from the door to the bus, the bus starts moving with the positive acceleration a. Use a coordinate system with x = 0 at the door of the stopped bus.
a) What is xman(t), the position of the man as a function of time? Answer symbolically in terms of the variables b, c, and t.
b) What is xbus(t), the position of the bus as a function of time? Answer symbolically in terms of a and t.
c) What condition is necessary for the man to catch the bus? Assume he catches it at time tcatch.
a. xman(tcatch) > xbus(tcatch)
b. xman(tcatch) = xbus(tcatch)
c. xman(tcatch) < xbus(tcatch)
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