How do we measure velocity?

Average velocity as change in position over elapsed time, its reading as the slope of a secant line, and shrinking intervals toward instantaneous velocity.

Active Calculus, How do we measure velocity?

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3 exercises

Activity 1.1.3

Each of the following questions concern $s(t) = 64 - 16(t-1)^2$ , the position function from Preview Activity.

Compute the average velocity of the ball on the time interval $[1.5,2]$ . What is different between this value and the average velocity on the interval $[0,0.5]$ ?
Use appropriate computing technology to estimate the instantaneous velocity of the ball at $t = 1.5$ . Likewise, estimate the instantaneous velocity of the ball at $t = 2$ . Which valu…

2.5

Activity 1.1.4

For the function given by $s(t) = 64 - 16(t-1)^2$ from Preview Activity, find the most simplified expression you can for the average velocity of the ball on the interval $[2, 2+h]$ . Use your result to compute the average velocity on $[1.5,2]$ and to estimate the instantaneous velocity at $t = 2$ . Finally, compare your earlier work in Activity.

2.5

Exercise 11

According to the U.S. census, the population of the city of Grand Rapids, MI, was 181,843 in 1980; 189,126 in 1990; and 197,800 in 2000.

Between 1980 and 2000, by how many people did the population of Grand Rapids grow?
In an average year between 1980 and 2000, by how many people did the population of Grand Rapids grow?
Just like we can find the average velocity of a moving body by computing change i…

2.5