Distance & Time Graphing Section 9.7

A distance - time graph shows how an object’s distance (how far it has gone) changes with time. When you’re using distance-time graphs the time is the independent variable (x axis) and the distance is the dependent variable (y axis).

Slope & Speed The SLOPE of the line on a dt-graph will give you the object’s speed. The greater the speed, the greater the slope of the line of a distance-time graph.

When you are analyzing slopes of graphs you are comparing the d during equal intervals of time. The slope of a distance-time graph is determined from the rise over the run (distance over time). Speed is determined from the slope of the best-fit straight line of a distance-time graph.

Solving for speed The straight line in the adjacent graph is what we call uniform or constant. A constant speed means that the object’s speed is the same at any given point on the line. When trying to determine the average speed using a graph such as this, you should use a large portion of the graph for your calculation. The darkened triangle represents the area used to determine the average speed.

2 (2, 6) 1 (1, 3) 2 1 y x

Analyzing d-t graphs d t slope = rise run V = = (9.0 – 2.0) km (9.0 – 2.0) min = 1.0 km/min ** The speed of an object in motion can be determined from the slope of a distance-time graph