# Average velocity when the interval has a domain

## Homework Statement

If a ball is thrown into the air with a velocity of 40 ft/sec, its height (in feet) after t seconds is given by
s(t) = 40t -16t^2.

Find the average velocity, vAV (t), of the ball over the time interval (t, 2), for 0 < t < 2.

## Homework Equations

change of x/change of t[/B]

## The Attempt at a Solution

Other questions were a breeze but this one stumped me. Am I just supposed to plug in 1 for t variable here? I feel like that doesn't make sense because the question before this was on the interval (1,2). I also thought maybe I should just replace the variable with the domain it has given me and write down a super long unsolved equation. Any help is appreciated thanks![/B]

MarkFL
I would let:

##\Delta t=2-t##

Now, the average velocity is the total displacement divided by the time elapsed:

##\overline{v}=\dfrac{\Delta s}{\Delta t}=?##

I would let:

##\Delta t=2-t##

Now, the average velocity is the total displacement divided by the time elapsed:

##\overline{v}=\dfrac{\Delta s}{\Delta t}=?##
but what value would go in for t here?

MarkFL
but what value would go in for t here?

##t## is not set to any specific value, all we know is ##0<t<2##, so your average velocity will depend on ##t##, that is, it will be a function of ##t##.

##t## is not set to any specific value, all we know is ##0<t<2##, so your average velocity will depend on ##t##, that is, it will be a function of ##t##.
So there will be no exact answer in the end wont there be a t variable?

MarkFL
So there will be no exact answer in the end wont there be a t variable?

Yes, the average velocity will depend on ##t##. It will give you a formula into which you can plug any allowed value of ##t## to find the average velocity corresponding to that value of ##t##.

Yes, the average velocity will depend on ##t##. It will give you a formula into which you can plug any allowed value of ##t## to find the average velocity corresponding to that value of ##t##.
how would I find what the change of position is if I have no first value of t to plug in?

MarkFL
how would I find what the change of position is if I have no first value of t to plug in?

You would use 2 as your final time and ##t## as your initial time, i.e.:

##\Delta s=s(2)-s(t)=?##