Aball is thrown into the air by a baby alien on a planet in the system of alpha centauri with a velocity of 29 ft/s. its height in feet after t seconds is given by y = 29 t − 22 t 2 . a. find the average velocity for the time period beginning when t=1 and lasting .01 s: .005 s: .002 s: .001 s: note: for the above answers, you may have to enter 6 or 7 significant digits if you are using a calculator.

Step-by-step explanation:

Now, in order to solve this problem, we need to use the average velocity formula:

From this point on, you have two possibilities, either you find each individual and input them into the formula, or you find a formula you can use to directly input the change of times. I'll take the second approach.

We know that:

and we also know that:

in order to find the final position, we can substitute this final time into the function, so we get:

so we can rewrite our formula as:

will always be the same, so we can start by calculating that, we take the provided function ans evaluate it for t=1s, so we get:

we can substitute it into our average velocity equation:

and we also know that the initil time will always be 1, so we can substitute it as well.

so we can now simplify our formula by expanding the numerator:

we can now simplify this to:

Now we can factor Δt to get:

and simplify

Which is the equation that will represent the average speed of the ball. So now we can substitute each period into our equation so we get:

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068