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:

answer: -8.2562234e+13