Why does dividing the final(chosen) height in a line by 2 give you the average height(y) in that line?

Question

I was taught, of course, that the average of something is the sum of all the parts divided by the number of those parts.

This is easy when it is a set of values(2, 6, 8) because its simply (2+6+8)/3 = 16/3 ≈ 5.33.

But when you have a line, you have an **infinite amount of values** divided by **infinity**, right?

So how is it even possible to take the average? And why can you simply divide it by 2 when its a line?

And then of course there is the question about the average of curves and whatnot…

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I feel so dumb, plz help me understand.

**Also this question comes from the idea that average velocity is half the final velocity**

In: 0

Answer 1

The average of the values in a line segment will be half of the starting value plus the ending value. For velocity call this (v_i + v_f )/2, which is the same as taking the average between just the final and initial velocities. This makes sense because to take the average of the whole line you can take the average between the initial and final values, then the average of the moment just after the initial value and the value just before the final value, and continue this until you get to the middle. All of these averages are the same, so the simplified formula works.