For a certain stretch of road the distance d in feet require

For a certain stretch of road, the distance d (in feet) required to stop a car that is traveling at a speed v (in mph) before the brakes are applied can be approximated by d(v)=0.06v^2+2v. Find the speed for which the car can be stopped within 250ft. write an inequality. Write a sentence explaining your labeled answer and give your answer in interval notation.

Solution

d(v)=0.06v^2+2v

the car can be stopped within 250ft :d < 250

d(v) < 250

0.06v^2 +2v < 250

0.06v^2 +2v -250 <0

3v^2/50 +2v -250 <0

(v-50)(3v +250) <0

-250/3<v < 50

Now neglecting the part where v<0 ; So, 0< v <50

If speed is less than 50 ft/sec the stopping distance can be less that 250 ft

V : (0, 50)