Understanding Position vs. Time Graphs

What is a Position vs. Time Graph?

A position vs. time graph is a graphical representation that shows how the position of an object changes over time. The y-axis of the graph represents the position of the object, while the x-axis represents the time.

Analyzing Position vs. Time Graphs

By examining a position vs. time graph, you can determine the following information:

• Object's position at a specific time: Read the y-value corresponding to a given time on the x-axis.
• Object's velocity: The slope of the graph represents the object's velocity. A steep slope indicates a high velocity, while a flat slope indicates a low or zero velocity.
• Object's acceleration: The curvature of the graph indicates the object's acceleration. A concave upward graph represents positive acceleration, while a concave downward graph represents negative acceleration.

Example: Sledding Down a Hill

Consider the following scenario: Randy is sledding down a hill while his sister Leslie observes from the top.

The correct graph that shows Randy's position as he moves away from his sister is option B Y. This graph represents the following sequence of events:

• At first, Randy moves at a constant speed down a nearly flat part of the hill (indicated by the straight line segment).
• Suddenly, the hill becomes much steeper, causing Randy to accelerate (indicated by the curved line segment).