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Graphing Motion

Graphing Motion. Equations are not the only way to go. We can often use graphs to quickly get a sense of what is happening as an object moves: Where is the object, and when. How fast is it moving and in what direction. By how much did it change it’s position.

patricia-whitley
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Graphing Motion

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  1. Graphing Motion

  2. Equations are not the only way to go. • We can often use graphs to quickly get a sense of what is happening as an object moves: • Where is the object, and when. • How fast is it moving and in what direction. • By how much did it change it’s position. • What’s the object’s acceleration. • Making and analyzing graphs is a cool skill, necessary for every burgeoning junior physicist.

  3. Consider the following data for a student walking to school. Plot the points on a graph with position (x) on the vertical axis, and time (t) on the horizontal axis. This is a position-vs-time graph, also known as a position graph, or an x-vs-t graph.

  4. Important! The graph does not show the object’s trajectory. Remember, the object is moving along the x- axis.

  5. Where did the object start? • In what direction did the object start moving? • At what time did the object cross the origin? • When was the object 5 m left of the origin? • How fast was the object moving at t = 35 s? • What total distance did the object cover? • What was the object’s average speed for the whole trip? • What was the object’s total displacement? • What was the object’s average velocity for the whole trip? x (m) t (s)

  6. What was the object’s velocity for 0 < t < 2 s? What was the object’s velocity for 2 < t < 4 s? What was the object’s velocity for 4 < t < 6 s?

  7. To go from a position graph to a velocity graph: Find the slopes… Then plot the slope values.

  8. Constant Acceleration On a position graph, constant acceleration is always a parabola.

  9. Average velocity for any time interval is the slope of the secant line over that time. Finding vavg from t= .75 s to t = 1.5 s Secant line

  10. What if we want instantaneous velocity?

  11. Instantaneous velocity at a particular time is the slope of the tangent line at that time. Finding v at t = .75 s Tangent line

  12. Slope = instantaneous velocity Tangent line Secant line Slope = average velocity

  13. Displacement is the area under the velocity-vs-time graph.

  14. Acceleration is the slope of the velocity graph.

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