"Calc. Labs

   "Waves

   "Parachute

   "Tower

     "Tower Lab

     "Math Rev.

     "Application

     "Survey

   "Radar

   "Rates

   "Area

   "Wing

   "Wrench

   "Hill

The applications of the concepts of average rate of change and instantaneous rate of change are quite numerous. In the following we present examples from USNA courses in physics and chemistry.  

In the SP211 course the author Serway presents the concepts of average and instantaneous velocity in Chapter 2 of the text. In Problem 7 the reader is asked specific calculations related to a given graph.

Problem 7. A position-time graph for a particle moving along the x-axis is shown in figure P2.7. (a) Find the average velocity in the time interval t = 1.5 s to t = 4.0 s. (b) Determine the instantaneous velocity at t = 2.0 s by measuring the slope of the tangent line shown in the graph. (c) At what value of t is the velocity zero?

Solution: The following was inserted from the web page solution sets from the Physics Department. You may link to this site at USNA PHYSICS SP211.

The graph above is from the text by McMurry and Fay (Chemistry, 2nd edition, Prentice-Hall, 1999) referenced by the USNA Chemistry Department Web Page for Plebe Chemistry Resources. 

The graph is from Chapter 12 on Chemical Kinetics. What kinds of rates of change observations could one make here?

1. We could note that the average rate of change of potential energy over the entire reaction would be negative, indicating an actual decrease over the entire time interval.
2. However, we can find various points in the reaction process where the instantaneous rate of change of potential is positive, and numerically large. These points would correspond to points on the curve where the tangent would have a large positive slope, indicating a sharp increase in potential energy.

USNA Mathematics Department
Comments to: Professor Carol G. Crawford, at cgc@nadn.navy.mil or Professor Mark D. Meyerson, at mdm@nadn.navy.mil