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 required to overcome air resistance, $P = F_d V$, involves the drag force $F_d = \frac{1}{2} C_d \rho V^2 A$. Substituting $F_d$ into $P$, we get $P = \frac{1}{2} C_d \rho V^2 A \cdot V$, which simplifies to $P = \frac{1}{2} C_d \rho V^3 A$. This shows that power as a function of velocity, $P(V)$, is a third-order function of $V$.

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 $F_{d}=\frac{1}{2} C_{d} \rho V^{2} A$