1. Problems Involving Drag

2. The resistive force due to motion through a fluid
Drag
The resistive force due to motion through a fluid

3. Low Speed/Small Object
Where c is a constant

4. Low Speed/Small Object Terminal Velocity
An object falling through a fluid will reach a terminal velocity when the weight of the object equals the drag force.

5. Low speed/Small Object Differential Equation
Which has a solution of the form
if the object starts from rest
and the general form of the equation is

7. As t  ∞, v  vt so
So the form of the solution is

8. Low speed/Small Object Acceleration
The acceleration is found by taking the derivative of the velocity function

10. High Speed/Large Object
Where c is a constant
The differential equation for this case is

11. High Speed/Large Object Terminal Velocity
where CD is the drag coefficient, ρ is the density of the fluid and A is the cross sectional area of the object

12. High Speed/Large Object Terminal Velocity
for a sphere , and