A scientist recorded the movement of an eagle and modeled it with the function x(t)=2t^2 where x is in

miles and t is in hours. What was the eagle's average velocity between times t = 5 and t = 7?

1 answer

The average velocity of the eagle between times t=a and t=b is given by the formula:

average velocity = (distance traveled between times a and b) / (time elapsed between times a and b)

To apply this formula, we need to find the distance traveled by the eagle between times t=5 and t=7. We can do this by subtracting the distance traveled at time t=5 from the distance traveled at time t=7:

distance traveled between t=5 and t=7 = x(7) - x(5)
= 2(7^2) - 2(5^2)
= 2(49) - 2(25)
= 48 miles

The time elapsed between t=5 and t=7 is 7 - 5 = 2 hours. Therefore, the average velocity of the eagle between times t=5 and t=7 is:

average velocity = (distance traveled between t=5 and t=7) / (time elapsed between t=5 and t=7)
= 48 / 2
= 24 miles per hour

Therefore, the eagle's average velocity between times t=5 and t=7 was 24 miles per hour.