Question #0996a

1 Answer
Jun 1, 2017

-80"ft"/"s"

Explanation:

We're asked to find the average rate of change (of position) with respect to the time interval [2,3]. This rate of change is the average velocity of the silver dollar, which is negative, as it is falling downward (assuming you take the positive y-axis as the "upward" direction).

The average velocity of the silver dollar is the rate of change of position with respect to time, given by the equation

v_(av-y) = (s_2-s_1)/(3"s"-2"s") = (Deltay)/(Deltat)

where

  • s is the position/height (in "ft") at times t = 2"s" (s_1) and t = 3"s" (s_2) (the change in y-position Deltay is always the final position minus the initial position, never the reverse), and

  • t is the time, in "s".

To find the positions at times t = 2"s" and t = 3"s", we simply plug in the values 2 and 3 in for the variable t in the equation:

t = 2

-16(2)^2 + 555 = color(red)(491"m"

t = 3

-16(3)^2 + 555 = color(green)(411"m"

So, plugging in these values into the average velocity equation, we have

v_(av-y) = (color(green)(411"ft")-color(red)(491"ft"))/(3"s"-2"s") = color(blue)(-80"ft"/"s"