If a rock is thrown upward on the planet x with a velocity of 10 m/s, then its height in meters t seconds later is given by s(t)=10t-2t^2. Find the average velocity on the time interval [1,3]

Question

kirbykirby · Answer

$$ avg.~velocity=\frac{s(3)-s(1)}{3-1}$$

anonymous · Answer

so would I put both of those in the equation? I do not understand the equation you gave me

kirbykirby · Answer

Maybe to give you some more background.. finding the average velocity is similar to finding the slope of a line. When finding the slope of a line with equation $y=mx+b$, you take 2 points $(x_1, y_1)$ and $(x_2, y_2)$ and find their slope as:
$$ slope=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-y_1}$$
Now, you can also write the equation of the line as: $f(x)=mx+b$, where $y=f(x)$. In this notation, the slope formula becomes: $$slope = \frac{f(x_2)-f(x_1)}{x_2-x_1} $$
Now, finding an average velocity is similar to finding the slope of a line. In fact the idea is that for any function (it doesn't have to be a line), you take 2 points, and then draw a connecting line through them. Then, the average velocity is going to be the slope of that connecting line. For example, your function $s(t)=10t-2t^2$ is a parabola which roughly looks like this: |dw:1409495486182:dw|