Question

Suppose that the distance D feet that a car travels in t seconds is given by d(t)=2t^2. Calculate the average speed (average rate of change.) in feet per second from t=5 to t=9. (An exact number.)

Answer 1

d(t)=2t^2. [5,9]
The average rate of change is calculated by the formula: d(t2) - d(t1) / t2 - t1
So plug in 5 as t1 and 9 as t2.
d(9) - d(5) / 9 - 5 =
(2×81) - (2×25) / 9 - 5 =
162 - 50 / 4 =
112 / 4 = 28
The average speed is 28 feet.