Question

For a certain model of car the distance d required to stop the vehicle if it is traveling at v mi/h is given by the formula d = v + v2 20 where d is measured in feet. kerry wants her stopping distance not to exceed 75 ft. at what range of speeds (in mi/h) can she travel? (enter your answer using interval notation.) c

Answer 1

Given that For a certain model of car the distance $d$ required to stop the vehicle if it is traveling at $v$ mi/h is given by the formula $d=v+\frac{v^2}{20}, where [tex]d$ is measured in feet.

If Kerry wants her stopping distance not to exceed 75 ft, then the range of speeds (in mi/h) can she travel is obtained as follows:

$v+ \frac{v^2}{20} \leq75 \\ \\ 20v+v^2\leq1,500 \\ \\ v^2+20v+100\leq1,500+100 \\ \\ (v+10)^2\leq1,600 \\ \\ |v+10|\leq\sqrt{1,600} \\ \\ -40\leq v+10\leq40 \\ \\ -40-10\leqv\leq v\leq40-10 \\ \\ -50\leq v\leq30$

Therefore, the range of speed she can travel is $v\leq30\ mi/hr$