Question

The height of an object launched upward from ground level is given by the function s(t) = -4.9t2 + 78.4t, where s(t) is the height in meters and t is the time in seconds. Arrange the time intervals in ascending order of the object's average velocity over the interval.

Time interval options:
8 to 11 seconds
6.5 to 8 seconds
2 to 2.5 seconds
4 to 4.5 seconds
3 to 3.5 seconds
9 to 11 seconds
9.5 to 10 seconds

Answer 1

To arrange the time intervals in ascending order of the object's average velocity over each interval, we need to calculate the average velocity for each interval.

Step-by-step explanation:

The height of an object launched upward from ground level is given by the function s(t) = -4.9t^2 + 78.4t, where s(t) is the height in meters and t is the time in seconds.

To arrange the time intervals in ascending order of the object's average velocity over each interval, we need to calculate the average velocity for each interval. The average velocity is given by the change in height divided by the change in time.

Let's calculate the average velocity for each interval:

1. 2 to 2.5 seconds: s(2.5) - s(2) / (2.5 - 2)
2. 3 to 3.5 seconds: s(3.5) - s(3) / (3.5 - 3)
3. 4 to 4.5 seconds: s(4.5) - s(4) / (4.5 - 4)
4. 6.5 to 8 seconds: s(8) - s(6.5) / (8 - 6.5)
5. 8 to 11 seconds: s(11) - s(8) / (11 - 8)
6. 9 to 11 seconds: s(11) - s(9) / (11 - 9)
7. 9.5 to 10 seconds: s(10) - s(9.5) / (10 - 9.5)

Now we can arrange these time intervals in ascending order based on the average velocity over each interval.