Solve the problem.
-For a motorcycle traveling at speed $v$ (in mph) when the brakes are applied, the distance d (in feet) required to stop the motorcycle may be approximated by the formula $d = 0.05 v ^ { 2 } + v$. Find the instantaneous rate of change of distance with respect to velocity when the speed is $40 \mathrm { mph }$.
A) 41 mph
B) 5 mph
C) 10 mph
D) 4 mph

Question

Quizplus · Accepted Answer

The instantaneous rate of change of distance with respect to velocity is the derivative of the distance function with respect to velocity. The derivative of $d = 0.05 v ^ { 2 } + v$ with respect to $v$ is $d' = 0.1 v + 1$. When the speed is $40 \mathrm { mph }$, the instantaneous rate of change of distance with respect to velocity is $d' = 0.1 (40) + 1 = 5 \mathrm { mph }$.

Solve the Problem vvv (In Mph) When the Brakes Are Applied, the Distance D

Solve the Problem $v$ (In Mph) When the Brakes Are Applied, the Distance D