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Visualizing motion by plotting distance against time on a coordinate plane.
Imagine you are a detective tracking a getaway car. If you only had a list of timestamps and distances, how could you tell at a glance exactly when the driver stopped for gas or when they hit the highway? The answer is hidden in the shape of a graph.
To visualize motion, we use a coordinate plane. In physics, we usually put Time on the horizontal x-axis because it is the independent variable—it keeps moving forward no matter what. Distance goes on the vertical y-axis because it is the dependent variable—how far you go depends on how much time has passed. Each point on the graph tells us exactly where an object was at a specific moment. When we connect these points, the resulting line tells a story about the object's movement.
Let's plot the motion of a turtle. 1. Look at the data: at seconds, distance is m. At seconds, distance is m. At seconds, distance is m. 2. Plot the points: , , and . 3. Draw a straight line through the points. 4. Notice that for every seconds, the turtle moves meter. The line is straight, meaning the speed is constant.
Quick Check
On a distance-time graph, which variable is plotted on the vertical y-axis?
Answer
Distance
The most important feature of a distance-time graph is the slope (the steepness of the line). In math, slope is . In physics, the 'rise' is the change in distance and the 'run' is the change in time. Since , the slope of the line is equal to the speed. A steeper line means the object is covering more distance in less time, which means it is moving faster. A flatter line means the object is moving slower.
Runner A and Runner B both start at the same time. 1. Runner A's line rises meters over seconds. Speed = . 2. Runner B's line rises meters over seconds. Speed = . 3. If you look at the graph, Runner A's line will be much steeper than Runner B's line because .
Quick Check
If the line on a distance-time graph gets steeper, what is happening to the object's speed?
Answer
The speed is increasing (the object is moving faster).
What happens if the line goes perfectly flat? A horizontal line means that as time (x-axis) continues to increase, the distance (y-axis) stays exactly the same. If your distance from the starting point isn't changing, you aren't moving! In physics terms, the object is at rest. The slope of a horizontal line is , which correctly shows that the speed is .
Imagine a -second trip: 1. From to seconds, the line rises from to meters. Speed = . 2. From to seconds, the line stays flat at meters. Speed = (the person stopped). 3. From to seconds, the line rises from to meters. Speed = . 4. The graph shows a 'step' shape, representing movement, a pause, and movement again.
What does the slope of a distance-time graph represent?
If a car is parked on the side of the road, how will its motion appear on a distance-time graph?
A steeper line on a distance-time graph indicates a slower speed.
Review Tomorrow
In 24 hours, try to sketch three lines: one for a fast object, one for a slow object, and one for an object that is not moving. Label your axes!
Practice Activity
Track your walk to school or a bus stop. Estimate your distance every minute for 5 minutes, then try to plot those points on a graph to see your 'speed story'.