Reading: Instantaneous Rate of Change and Tangent Lines
Instantaneous Velocity
Suppose we drop a tomato from the top of a 100 foot building and time its fall (see figure 1). Some questions are easy to answer directly from the table given in figure 1:- How long did it take for the tomato n to drop 100 feet? 2.5 seconds
- How far did the tomato fall during the first second? 100 – 84 = 16 feet
- How far did the tomato fall during the last second? 64 – 0 = 64 feet
- How far did the tomato fall between t =.5 and t = 1? 96 – 84 = 12 feet
- What was the average velocity of the tomato during its fall? Average velocity =
- What was the average velocity between t = 1 and t = 2 seconds? Average velocity = = = =
- How fast was the tomato falling 1 second after it was dropped?
Average velocity = = slope of the secant line through 2 points.
Instantaneous velocity = slope of the line tangent to the graph.