# Average Value of a Function and average velocity

Hey quick question regarding the average value of a function;
What is the difference in finding the average velocity over an interval given the position function, s(t), and the velocity function, v(t)?

I don't get it?

Mark44
Mentor
Hey quick question regarding the average value of a function;
What is the difference in finding the average velocity over an interval given the position function, s(t), and the velocity function, v(t)?

I don't get it?

v(t) is a function that tells you the velocity at any instant t. So for example, if you drive somewhere in a car, it might be that v(5 min) = 25 mph, v(10 min) = 60 mph, and v(15 min) = 0 mph.

The average velocity is defined as 1/(total time) * an integral of the velocity. If you were able to stay at the same velocity throughout some time interval, the average velocity would be identical to v(t) at any time in that interval.

v(t) is a function that tells you the velocity at any instant t. So for example, if you drive somewhere in a car, it might be that v(5 min) = 25 mph, v(10 min) = 60 mph, and v(15 min) = 0 mph.

The average velocity is defined as 1/(total time) * an integral of the velocity. If you were able to stay at the same velocity throughout some time interval, the average velocity would be identical to v(t) at any time in that interval.

I still don't see the difference though?

Mark44
Mentor
v(t) can be different at each number in the interval. Average velocity is in some sense the average (or mean) of all of the different values of v(t). Instead of calculating the average like you would for a set of discrete values by adding them together and dividing by how many numbers you had, what happens instead is that you integrate (which is akin to addition) and divide by the length of the interval.

v(t) can be different at each number in the interval. Average velocity is in some sense the average (or mean) of all of the different values of v(t). Instead of calculating the average like you would for a set of discrete values by adding them together and dividing by how many numbers you had, what happens instead is that you integrate (which is akin to addition) and divide by the length of the interval.

That makes more sense. Thank you!!! 