Question

question
part 2 of 3
completed: 1 of 10 | my score: 0.33/10 pts (3.33%)
limits graphs
consider the position function ( s(t) = -16t^2 + 120t ) 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 ( (2, s(2)) ). determine the slope of the secant line and explain its relationship to the moving object.
save

Explanation:

Step1: Find s(0.25) and s(2)

First, calculate \( s(0.25) \):
\( s(0.25) = -16(0.25)^2 + 120(0.25) \)
\( = -16(0.0625) + 30 \)
\( = -1 + 30 = 29 \)

Next, calculate \( s(2) \):
\( s(2) = -16(2)^2 + 120(2) \)
\( = -16(4) + 240 \)
\( = -64 + 240 = 176 \)

Step2: Use slope formula

The slope \( m \) of the secant line through \( (x_1, y_1) = (0.25, 29) \) and \( (x_2, y_2) = (2, 176) \) is:
\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{176 - 29}{2 - 0.25} \)
\( = \frac{147}{1.75} = 84 \)

Answer:

The slope of the secant line is \( \boldsymbol{84} \). This slope represents the average velocity of the object between \( t = 0.25 \) and \( t = 2 \) seconds.