The drag force acting on a car can be modeled using the following function: $$F _ { d } = \frac { 1 } { 2 } C _ { d } \rho {{ V } ^ { 2 }} A$$
where $F _ { d } =$ drag force
$C _ { d } =$ drag coefficient
$\rho =$ air density
$V =$ speed of car relative to air
$A =$ frontal area of car
The power $P$ required to overcome air resistance can be modeled according to $P = F _ { d } V$.
When analyzing power as a function of velocity $P ( V )$, what order is the resulting function?
A)first order
B)second order
C)third order
D)none of the above

Question

The drag force acting on a car can be modeled using the following function: $$F _ { d } = \frac { 1 } { 2 } C _ { d } \rho  {{ V } ^ { 2 }} A$$
where $F _ { d } =$ drag force
$C _ { d } =$ drag coefficient
$\rho =$ air density
$V =$ speed of car relative to air
$A =$ frontal area of car
The power $P$ required to overcome air resistance can be modeled according to $P = F _ { d } V$.
When analyzing power as a function of velocity $P ( V )$, what order is the resulting function?
A)first order
B)second order
C)third order
D)none of the above

Quizplus · Accepted Answer

The power function $P(V) = F_d V = \frac{1}{2} C_d \rho V^2 A \cdot V$ simplifies to $P(V) = \frac{1}{2} C_d \rho A V^3$, which is a third-order function in terms of velocity $V$.

The Drag Force Acting on a Car Can Be Modeled Fd=12CdρV2AF _ { d } = \frac { 1 } { 2 } C _ { d } \rho {{ V } ^ { 2 }} AFd​=21​Cd​ρV2A

The Drag Force Acting on a Car Can Be Modeled $F _ { d } = \frac { 1 } { 2 } C _ { d } \rho {{ V } ^ { 2 }} A$