Question

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.1

Answer 1

Hmm -- your school subject appears to be math, not chabot college.

Answer 2

s = sin (pi t) is a sin function starting at (0,0)the period T is when pi t = 2 pi
or in other words when t = 2

when t = .5
s = sin (pi/2) = 1

at t=0 the slope = cos 0 = 1
at t = .5 the slope = cos pi/2 = 0
in other words the function climbs up from (0,0) to a peak at (.5,1) and then heads down