Question

The distance traveled, in feet, of a ball dropped from a tall building is modeled by the equation d(t) = 16t2 where d equals the distance traveled at time t seconds and t equals the time in seconds. What does the average rate of change of d(t) from t = 2 to t = 5 represent?
Answer Choices:

a.The ball travels an average distance of 112 feet from 2 seconds to 5 seconds.

b.The ball falls down with an average speed of 48 feet per second from 2 seconds to 5 seconds.

c.The ball falls down with an average speed of 112 feet per second from 2 seconds to 5 seconds.

d.The ball travels an average distance of 48 feet from 2 seconds to 5 seconds.

Answer 1

Average rate of change = (d(5) - d(2)) / (5 - 2) = (16(5)^2 - 16(2)^2) / 3 = 336 / 3 = 112.

Therefore, the average rate of change of d(t) from t = 2 to t = 5 represents that the ball travels an average distance of 112 feet from 2 seconds to 5 seconds.