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Motion and Force. Chapter Three: Motion. 3.1 Position and Velocity 3.2 Graphs of Motion 3.3 Acceleration. Investigation 3B. Position, Speed and Time Graphs. What kind of motion happens when an object rolls down a hill?. 3.2 The position vs. time graph.
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Chapter Three: Motion • 3.1 Position and Velocity • 3.2 Graphs of Motion • 3.3 Acceleration
Investigation 3B Position, Speed and Time Graphs • What kind of motion happens when an object rolls down a hill?
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 weakrelationship, • 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 slopeis 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?
3.2 Speed vs. time graphs These graphs each show the same event. What differences do you notice?
3.2 Calculating distance • A speed vs. time graph can also be used to find the distancethe object has traveled.