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A bus is traveling at 80feet per second. suddenly, the driver appies the brakes. The speed of the braking bus after t seconds is given by f=80-20t^2.

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You need to find when the speed is zero, this would mean the bus comes to a complete stop. Since the speed after braking is given by:
setting this equal to zero yields:
80-20t2=0 Or 80=20t2, which leads to 
t2=80/20=4, from which it is easy to see that
t=2 seconds