Investigation 3B
• What kind of motion happens when an object rolls down a hill?
Position, Speed and Time Graphs
3.2 The position vs. time graph
• Motion graphs are an important tool used to show the relationships between position, speed, and time.
A runner can learn more about performance by studying data and graphs.
3.2 The position vs. time graph
• Position vs. time data tells you the runner’s position at different points in time.
• The runner is at 50 meters after 10 sec., 100 meters after 20 sec. and 150 meters at 30 sec.
3.2 Graphs show relationships
• A good way to show a relationship between two variables is to use a graph.
• A graph makes it easy to see if changes in one variable cause changes in the other variable (the effect).
3.2 The position vs. time graph
• To graph data, you put position on the vertical (y) axis .
• Time goes on the horizontal (x) axis.
• Data are plotted between x and y axis.
3.2 The position vs. time graph
• An object moving at a constant speed always creates a position vs. time graph that is a straight line.
3.2 The position vs. time graph
• Two variables may have:– a strong relationship, – a weak relationship,– or no relationship at all.
3.2 Graphs show relationships
• This table shows how quickly the car gets from A to B as the angle of the track changes.
3.2 Graphs show relationships
• If we plot the data on a graph, what kind of relationship does the graph show?
3.2 Four steps to make a graph
Step 1: Choose which will be the dependent and independent variables. The dependent variable goes on the y-axis and the independent variable goes on the x-axis.
Step 2: Make a scale for each axis by counting boxes to fit your largest value. Count by multiples of 1, 2, 5, or 10.
Step 3: Plot each point by finding the x-value and drawing a lin upward until you get to the right y-value.
Step 4: Draw a smooth curve that shows the pattern of the points. Do not just connect the dots.
3.2 Reading a graph
• A graph can give you an accurate answer even without doing the experiment.
• Students doing an experiment measured the speed of the car at 20, 40, 60, and 80 cm positions.
• They want to know the speed at 50 cm.
3.2 Slope
• You can use position vs. time graphs to quickly compare the speeds of different objects.
A steeper line on a position vs. time graph means a faster speed.
3.2 Slope
• The “steepness” of a line is called its slope.
• Visualize a triangle with the slope as the hypotenuse.
• The rise is equal to the height of the triangle.
• The run is equal to the length along the base of the triangle.
3.2 Slope
• The slope is the ratio of the “rise” (vertical change) to the “run” (horizontal change).
• The slope is therefore a distance divided by a time, which equals speed.
3.2 Speed vs. time graphs
• The position vs. time graph has position on the y-axis and time on the x-axis.
Which runner has the fastest constant speed?