When air resistance is represented by $F(v) = -kv^n$, what does $n$ actually mean? I know that $k$ is a constant dependent on the shape of the object and the density of the air, but what things does $n$ depend on?
 A: $F=-kv^n$ is a formula that sometimes describes the dependence of resistive force on the body's speed. The value of $n$ depends on the nature of the resistive force... At low speeds the resistive force is viscous (needed to make layers of fluid slide over each other), and $n=1$, whereas at considerably higher speeds the main resistive force is that needed to give momentum to the fluid ahead of the body to push it out of the way. In that case $n=2$.
The above is highly simplified. For example there are intermediate speeds at which neither formula holds.
A: $F(v) = -kv^n$
This is a resistive force and this n is just a number which implies Resistance to a moving object is directly proportional to its velocity's nth power.
For example generally for a freely falling object F=-kv
So we may state deceleration due to F is -kv/m and further make calculations by what we are asked like for reaching terminal velocity we need this and integrate it to some term.
So basically n is just nothing more than a number which varies as per question.
