A car is traveling at 100 ft/s when the driver suddenly applies the brakes (x =0, t = 0). The position function of the skidding car is "x(t)=100t-5t^2."
How far and for how long does the car skid before it comes to a stop?
The car comes to a stop when "x'(t)=0."
"x'(t)=0=>100-10t=0=>t=10\\ s"
"x(10)=100(10)-5(10)^2=500\\ ft"
The car comes 500 ft to a stop. Time to stop is 10 s.
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