GRAPHS OF MOTION

Position vs. Time Graphs

An object moving at a constant speed always creates a straight line on a position vs. time graph.• You can use the formula v =d/t to calculate the speed. • Example: Dividing 50 meters by 10 seconds tells you her constant speed was 5 meters per second.

Relationships

In a strong relationship, large changes in one variable make similarly large changes in the other variable.

In a weak relationship, large changes in one variable cause only small changes in the other.

When there is no relationship, the graph looks like scattered dots.

Calculating Speed From a Position vs. Time Graph

A steeper line on a position vs. time graph means a faster speed.

The “steepness” of a line is called its slope. The slope is the ratio of the rise (vertical change) divided by run (horizontal change).

The slope of the graph is therefore the distance traveled divided by the time it takes, or the speed.

The speed vs. time graph has speed on the y-axis and time on the x-axis.

Speed vs. Time Graph

A speed vs. time graph can also be used to find the distance the object has traveled.

Remember, distance is equal to speed multiplied by time (d=s*t).

The area of the rectangle is equal to its length times its height.

On the graph, the length is equal to the time and the height is equal to the speed.

Therefore, the area of the graph is the speed multiplied by the time. This is the distance the runner traveled.

Christopher’s Road Trip

Christopher borrowed his mother’s car to run a quick errand. Use the graph to answer questions about his trip.

1. How far did Christopher’s car travel between points A and B? 2. How much time did it take for Christopher to travel from

point A to point B? 3. Describe the motion of Christopher’s car between points B

and C. 4. What is the speed of the car between points A and B? 5. How would you describe the slope of the graph between

points D and E? 6. What does a negative slope tell you about the direction the

car is traveling? 7. Is Christopher traveling faster between points A and B or

points F and G? How can you tell? 8. What happens at point G?