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 1

The average rate of change of height is speed.

The average rate of change of d(t) on t ∈ [2, 5] represents the ball's average speed over that interval of time.

Answer 2

Find out what does the average rate of change of d(t) from t = 2 to t = 5 represent .

To prove

Formula

`Average\ rate\ of\ change = (d(5) - d(2))/(change\ in\ time)`

As given

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 .

Now

d(5) = 16 × 5 × 5

= 400 feet

d(2) = 16 × 2 × 2

= 64 feet

Now

Change in time = 5 - 2

= 3 second

put all the values in the above formula

`Average\ rate\ of\ change = (400 - 64)/(3)`

`Average\ rate\ of\ change = (336)/(3)`

Average rate of change is 112 feet/second.