Questions: Consider the position function s(t)=-16 t^2+100 t representing the position of an object moving vertically along a line. Sketch a graph of s with the secant line passing through (0.25, s(0.25)) and ( 3, s(3) ). Determine the slope of the secant line and explain its relationship to the moving object.
Sketch the graph of s with the secant line. Choose the correct graph below.
A.
B.
C.
The slope of the secant line is msec= (Type an integer or a decimal.)
Transcript text: Consider the position function $s(t)=-16 t^{2}+100 t$ representing the position of an object moving vertically along a line. Sketch a graph of $s$ with the secant line passing through $(0.25, s(0.25))$ and ( $3, \mathrm{~s}(3)$ ). Determine the slope of the secant line and explain its relationship to the moving object.
Sketch the graph of $s$ with the secant line. Choose the correct graph below.
A.
B.
C.
The slope of the secant line is $\mathrm{m}_{\mathrm{sec}}=$ $\square$ (Type an integer or a decimal.)
Solution
Solution Steps
Step 1: Calculate s(0.25) and s(3)
Given the position function s(t) = -16t² + 100t, we substitute t = 0.25 and t = 3 into the function: