For a certain stretch of road, the distance d (in feet) required to stop a car t

Question

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) =0.05v^2+2.5v.
Find the speed for which the car can be stopped within 250 feet - this means write an inequality. Make sure to show all your work. Be sure to restrict the domain appropriately.
  Write a sentence explaining your labeled answer and give your answer in interval notation. 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) =0.05v^2+2.5v.
Find the speed for which the car can be stopped within 250 feet - this means write an inequality. Make sure to show all your work. Be sure to restrict the domain appropriately.
  Write a sentence explaining your labeled answer and give your answer in interval notation.
Find the speed for which the car can be stopped within 250 feet - this means write an inequality. Make sure to show all your work. Be sure to restrict the domain appropriately.
  Write a sentence explaining your labeled answer and give your answer in interval notation.

Explanation / Answer

given distance required for stopping a car travelling at a speed of 'v' mph is

d(v)=0.05v^2+2.5v

to stop the car within the distance of 250ft, we must have

d(v)=0.05v^2+2.5v <250

multiplying bothsides with 100, we get

5v^2+250v<25000

dividing bothsides by 5

v^2+50v<5000

rearranging the euation

v^2+50v-5000<0

(v-50)(v+100)<0

as 'v' is always greater than or equal to '0'

v-50<0

so, for v<50mph the car will stop within a distance of 250 feet

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