Graphical Interpretation of Motion in One Dimension

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Presentation transcript:

Graphical Interpretation of Motion in One Dimension

Why Graphs? Graphing gives us a visual “picture” of a mathematical relationship Slopes of lines, x- or y-intercepts, and areas under curves have meaning As determined by the equation representing the physical quantity

Graphing Tips Label axes (including units) Scale Appropriate size to allow analysis Mark scale on axes Draw a line of “best fit” Don’t simply connect the dots!!

Line of Best Fit • • • • Analyze data based on “best fit” • Displacement (m) • • Analyze data based on “best fit” • Time (s)

Describe the motion of this object 30 20 Displacement (m) 10 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Time (s) Describe the motion of this object

Graphical Interpretation of Velocity Velocity can be determined from a position-time graph Average velocity equals the slope of the line joining the initial and final positions An object moving with a constant velocity will have a graph that is a straight line

Average Velocity, Constant The straight line indicates constant velocity The slope of the line is the value of the average velocity

Average Velocity, Non Constant The motion is non-constant velocity The average velocity is the slope of the blue line joining two points

Instantaneous Velocity on a Graph The slope of the line tangent to the position-vs.-time graph is defined to be the instantaneous velocity at that time The velocity at any specific point in time The instantaneous speed is defined as the magnitude of the instantaneous velocity

How would I calculate the average speed from t = 1.0s to t = 7.0s? 30 20 displacement (m) 10 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Time (s) How would I calculate the average speed from t = 1.0s to t = 7.0s?

Uniform Velocity Uniform velocity is constant velocity The instantaneous velocities are always the same All the instantaneous velocities will also equal the average velocity

Interpreting Motion Graphs Area Under Curve = Displacement v t

How would I calculate the total displacement of this object? 30 20 velocity (m/s) 10 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Time (s) How would I calculate the total displacement of this object?

Interpreting Motion Graphs Area Under Curve = Speed a t