Consider the position function s(t)=sin((pi)(t)) representing the position of an object moving along a line on the end of a spring. Sketch a graph of s with the secant line passing through (0,s(0)) and (0.5,s(0.5)). Determine the slope of the secant line and its relationship to the moving object.

Answer 1

clearly,
s(0) = 0
s(1/2) = 1

So, the line is y=2t.

since t is time and y is position, say, cm, then the slope of the line (cm/s) is the average velocity during the interval [0,0.5]

See

http://www.wolframalpha.com/input/?i=plot+y%3Dsin%28pi*x%29%2C+y%3D2x

Answer 2

Steve, I already tried 0.5 and that was incorrect.

Answer 3

what do you mean you "tried 0.5"? Tried for what? In my solution, the slope is 2, not 1/2.