1. Aim: How do we explain air resistance?

2. Reading Passage
Consider the equation: 10-y=8. When we solve this equation, we find that y=2. In other words, y is a number. In all of the equations we have seen in physics, the variables have been represented by numbers. However, in a differential equation, this is no longer the case. Consider the equation: dx/dt= 5x(t). This equation is a differential equation which states that the number 5 multiplied by a function x(t) is equal to the derivative of the function x(t). When we solve this equation, we are not solving for an unknown number but for an unknown function. In this case x(t)=e5t. You can test to see that this function satisfies the differential equation.

3. Velocity function for object before it hits terminal velocity
Write a differential equation under the influence of drag force bv. m(dv/dt)=mg-kv In other words, what is the net force on a falling body equal to at any specific time. Assume the object was dropped from rest. ma=mg-kv
mg – kv = m dv/dt

4. Solution to Differential Equation
v(t) = mg/kb(1 – e (-b/m)t ) Test this function for v(0) and v(infinity) Prediction: What should the initial velocity be? 0 What should the final velocity be? Terminal Velocity