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.)

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.)
failed

Solution

failed
failed

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:

s(0.25) = -16(0.25)² + 100(0.25) = -16(0.0625) + 25 = -1 + 25 = 24

s(3) = -16(3)² + 100(3) = -16(9) + 300 = -144 + 300 = 156

So the two points are (0.25, 24) and (3, 156).

Step 2: Identify the correct graph

The correct graph should pass through the points (0.25, 24) and (3, 156). Graph A is the correct graph.

Step 3: Calculate the slope of the secant line

The slope of the secant line, msec, is given by the change in s divided by the change in t:

msec = (s(3) - s(0.25)) / (3 - 0.25) = (156 - 24) / (2.75) = 132 / 2.75 = 48

Final Answer

The correct graph is A, and the slope of the secant line is 48.

Was this solution helpful?
failed
Unhelpful
failed
Helpful