a) You can catch the bus after 1.8 s or 10 s
b) The maximum time that you can wait is 1.42 s
Explanation:
a)
The motion of the bus is an accelerated motion, so its position at time t can be written as

where
d = 9.0 m is the initial distance between you and the bys
is the acceleration of the bus
Substituting,
(1)
The motion of the person is uniform, so its position at time t is

where
v = 5.9 m/s is the constant speed
Substituting,
(2)
The person reaches the bus when

Re-arranging and solving for t,

(3)
Which gives two solutions:
t = 1.8 s
t = 10 s
b)
If the person waits a time t' before starting to run, then the position of the person is given by

So the equation to solve becomes:

This means that the discriminant of the solution of this second-order equation is

In order for the person to still catch the bus, there must be at least 1 real solution to the equation, so the discrimant must be at least zero:

And solving for t',

Learn more about accelerated motion:
brainly.com/question/9527152
brainly.com/question/11181826
brainly.com/question/2506873
brainly.com/question/2562700
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