Average velocity Consider the position function s(t)=-16...

Average velocity Consider the position function $s(t)=-16 t^{2}+100 t$ representing the position of an object moving along a line. Sketch a graph of $s$ with the secant line passing through $(0.5, s(0.5))$ and $(2, s(2)) .$ Determine the slope of the secant line and explain its relationship to the moving object.

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Key Concepts

Position Function

A position function represents the location of an object as a function of time. In the context of motion along a line, it maps each time value to a specific position, allowing one to track or predict the object's whereabouts over time. This function is crucial for analyzing motion, understanding displacement, and setting the stage for further calculations like velocity.

Secant Line

A secant line is a straight line that passes through two distinct points on the graph of a function. It is used to approximate the average rate of change between those two points. In problems related to motion, the secant line between two points on a position-time graph visually represents the average velocity over the time interval between those points.

Average Velocity

Average velocity is defined as the total displacement divided by the total time taken, which mathematically corresponds to the slope of the secant line on a position-time graph. It measures the overall change in position of an object over a specified interval and provides a simple measure of how fast and in which direction the object has moved over that time period.

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