Introduction:
The basic equations are:
Since we are dealing only with one-dimensional motion, vector signs are not needed. Signs can indicate the vector nature. When two and three-dimensional motion is considered, vector notation (including unit vectors) will have to be used. The only derivatives you'll need to know for now are:
You'll also need the product and quotient rules. In one problem, you have to find the velocity and position from the acceleration. To do so, you need to separate the variables and integrate:
You may have to do the same thing for dx/dt = v to get the position. The initial velocity (that is, the velocity at t = 0) is usually designated as vo.
Problem 49 is a "related rates" problem. For example, you will have to differentiate something like this:
Examples:
Example 1: Differentiation to find velocity and acceleration
Example 2: A related rates problem - a pulley system
Example 3: Another related rates problem - pulling a car out a ditch
Example 4: Obtaining position and velocity from acceleration (not covered in the chapter - optional topic)