The following examples refer to Bradley's Calculus.
Rates of Change are important in understanding rectilinear motion (displacement, velocity, and acceleration).
Examples:
- pg. 114 (Section 2.4): Example #3
- pg. 118 (Section 2.4): #24, #25, #26, #27
A falling body problem is another example of rectilinear motion
Examples:
- pg. 116 (Section 2.4): Example #4
- pg. 118 (Section 2.4): #30, #31, #32, #34
- pg. 119 (Section 2.4): #40, #48
The chain rule must be understood because in many situations, a quantity is given as a function of one variable, which, in turn, can be thought of as a function of a second variable
Examples:
- pg. 128-129 (Section 2.6): #52, #53, #62
Derivatives represent rates of change of two or more quantities that can be related to each other.
Examples:
- pg. 138 (Section 2.7): Example #3
- pgs. 141-142 (Section 2.7): #10-15, #33
The following examples refer to Young and Freedman's University Physics.
Work is the integral of force which can be written as the integral of mass times acceleration or the integral of mass times veloctiy times the derivative of velocity with respect to distance. All of these are integrated with respect to distance. The following examples use this relationship.
Examples:
Instantaneous power is the derivative of work with respect to time.
Two different objects thrown at the same time to different heights have the same speed at a given height which can be seen on pg. 200 (Example 7-3)
Examples:
- pg. 219 (7-3)
The potential energy curve for a spring is a parabola (pg. 205 Figure 7-11)
Examples:
- pg. 222 (7-38) involves analysis of a graph and the concepts of equilibrium
- pg. 220 (7-18); one could also produce a graph
