An astronaut drops a rock into a crater on the moon. The distance, d (t), in meters, the rock travels after t seconds can be modeled by d (t) = 0.8t^2. What is the average speed, in meters per second, of the rock between 5 and 10 seconds after it was dropped?

Given:

d (t) = 0.8t²

t = 5 seconds

d (5) = 0.8 * 5² = 0.8 * 25 = 20

t = 10 seconds

d (10) = 0.8 * 10² = 0.8 * 100 = 80

20 meters / 5 seconds = 4 meters per second

80 meters / 10 seconds = 8 meters per second

4 meters per second + 8 meters per second = 12 meters per second

12 meters per second / 2 = 6 meters per second.

6 meters per second is the average speed of the rock between 5 and 10 seconds after it was dropped.