Question

A car is travelling at 100 ft/sec when the driver suddenly applies the brakes. The position
function of the skidding car is

Answer 1

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 $x'(t)=0.$

$$x'(t)=(100t-5t^2)'=100-10t$$

$$x'(t)=0=>100-10t=0=>t=10\ s$$

$$x(10)=100(10)-5(10)^2=500\ ft$$

The car comes 500 ft to a stop. Time to stop is 10 s.