Question

A student is running to catch the bus, which is stopped at the bus stop. The student is
running at a constant velocity of 6 m/s: she cannot run any faster. When the student is still
80 m from the bus, it starts to pull away. The bus moves with a constant acceleration of
0.20 m/s^2.
a. For how much time and how far will the student have to run before she catches up
with the bus?
b. When she reaches the bus, how fast will the bus be traveling?

c. Sketch a graph showing x(t) for both the student and the bus. Take x=0 as the
initial position of the student.
d. The equations you used in (a) to find the time have a second solution, corresponding
to a later time for which the student and bus will be again at the same place if they
continue their specified motion. Explain the significance of this second solution.
How fast will the bus be traveling at this point?
e. If the student’s constant velocity is 4 m/s, will she catch the bus?
f. What is the minimum speed the student must have to just catch up with the bus?
g. How long and how far will she have to run in case (f)?

Answer 1