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

d(5) = 0.8*5² = 0.8 * 25 = 20
d(10) = 0.8*10² = 0.8 * 100 = 80

Average speed = distance traveled / time of travel
Average speed = 20 meters / 5 seconds = 4 meters per second

Average speed = 80 meters / 10 seconds = 8 meters per second

4 mps + 8 mps = 12 mps 
12 mps / 2 = 6 mps the average speed in meters per second between 5 and 10 seconds.