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 Homework Statement:

popular web video shows a jet airplane, a car, and a motorcycle
racing from rest along a runway. Initially
the motorcycle takes the lead, but then the jet takes the lead,
and finally the car blows past the motorcycle. Here let’s focus
on the car and motorcycle and assign some reasonable values
to the motion.The motorcycle first takes the lead because its
(constant) acceleration am = 8.40 m/s2 is greater than the car’s
(constant) acceleration ac = 5.60 m/s2, but it soon loses to the
car because it reaches its greatest speed vm =58.8 m/s before
the car reaches its greatest speed vc =106 m/s. How long does
the car take to reach the motorcycle?
 Relevant Equations:

[tex]\frac{1}{2}ac{t^2} = \frac{1}{2}\frac{{{v^2}m}}{{am}} + (t  7.00s)[/tex]
((1/2)act^2=(1/2)(vm^2/am)+(t7.00s)
Sample Problem 2.04 Drag race of car and motorcycle
I was following all the way up to using the quadratic equation for this problem...(please see img for a more detailed attempt at a solution.)
So I may have simplified incorrectly here:
but I came up with
2.8t^2(58.8)t+408.1=0
but when filling in
a=2.8
b=58.8
c=408.1
in the quadratic equation to find "t" The root would be negative. So I'm stuck. The answer to the example problem is 4.44 s and t 16.6 s which 16.6 would be the correct answer for t, I just am stuck at how they got these answers from the quadratic equation.
I was following all the way up to using the quadratic equation for this problem...(please see img for a more detailed attempt at a solution.)
So I may have simplified incorrectly here:
but I came up with
2.8t^2(58.8)t+408.1=0
but when filling in
a=2.8
b=58.8
c=408.1
in the quadratic equation to find "t" The root would be negative. So I'm stuck. The answer to the example problem is 4.44 s and t 16.6 s which 16.6 would be the correct answer for t, I just am stuck at how they got these answers from the quadratic equation.
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