Navigation
Analyze the steepness of lines on a graph to compare how fast different objects are moving.
If you saw two lines on a graph—one shooting up like a rocket and one crawling like a snail—could you tell who wins the race without seeing a single number?
In physics, a Position-Time Graph tells a story of movement. The horizontal axis () represents Time, and the vertical axis () represents Position (or distance). The most important feature of this graph is the slope, or the 'slant' of the line. The rule is simple: the steeper the line, the faster the object is moving. A very steep line means the object is covering a lot of distance in a very short amount of time. Conversely, a shallow or 'flatter' line means the object is moving slowly, taking a long time to cover the same distance.
Quick Check
If Line A is much steeper than Line B on a distance-time graph, which object is moving slower?
Answer
Line B is moving slower because its lower steepness indicates a lower speed.
A snail starts at meters. After seconds, it has moved meters. Let's find its speed. 1. Identify Point 1: 2. Identify Point 2: 3. Apply the formula: 4. Calculate: .
Real-world motion isn't always a straight line. Graphs often have different segments. A horizontal line (flat) means the distance isn't changing even though time is passing—this means the object is at rest (speed = ). A straight diagonal line means constant speed. If you see a line that curves upward, becoming steeper and steeper, it means the object is accelerating (speeding up)!
A truck drives in , stops for to drop a package, then drives another in . 1. Segment 1 Speed: . 2. Segment 2 (The Stop): The line is flat. Speed is . 3. Segment 3 Speed: . Even though the truck stopped, its speed during the moving segments was the same because the steepness of those two lines is identical.
Quick Check
What does a perfectly horizontal line on a position-time graph represent?
Answer
It represents an object at rest (zero speed).
Runner A starts at the mark moving at . Runner B starts at the mark (a head start) but moves at . 1. Runner A's line: 2. Runner B's line: 3. On a graph, Runner A's line is steeper. Eventually, Runner A's line will cross Runner B's line. That intersection point is exactly when and where Runner A passes Runner B!
If a graph shows a line going from to , what is the speed?
Which of the following describes an object that is not moving?
On a position-time graph, a steeper line always represents a faster object.
Review Tomorrow
Tomorrow morning, try to sketch a graph of your walk to school. Where did you move fast (steep)? Where did you stop at a crosswalk (flat)?
Practice Activity
Find a graph in your textbook and calculate the slope of three different segments to see which part of the journey was the fastest.