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Understanding Average Speed, Velocity, and Acceleration in Motion

This guide explains the concepts of average speed, average velocity, and average acceleration. Average speed measures how fast a particle moves, while average velocity considers the displacement over time, always with direction. Average acceleration indicates how quickly the velocity changes over time. Various sample problems illustrate these concepts, including calculating average velocity for a motorist driving north and determining average acceleration. Additionally, graphical interpretations help in understanding average velocity and speed from position versus time plots.

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Understanding Average Speed, Velocity, and Acceleration in Motion

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  1. September 3, 2010 Average Speed, Velocity, Acceleration

  2. Average Speed and Average Velocity • Average speed describes how fast a particle is moving. It is calculated by: • Average velocity describes how fast the displacement is changing with respect to time: always positive sign gives direction

  3. Average Acceleration • Average acceleration describes how fast the velocity is changing with respect to time. The equation is: sign determines direction

  4. Sample problem: A motorist drives north at 20 m/s for 20 km and then continues north at 30 m/s for another 20 km. What is his average velocity? 24 m/s

  5. Sample problem: It takes the motorist one minute to change his speed from 20 m/s to 30 m/s. What is his average acceleration? 0.167 m/s2

  6. B A Dx Dt Average Velocity from a Graph x t

  7. A x B Dx Dt t Average Velocity from a Graph

  8. B A Dx Dt Average Acceleration from a Graph v t

  9. x(m) 3 2 1 0 A -1 B -2 -3 0 0.1 0.2 0.3 0.4 0.5 t(s) • Sample problem: From the graph, determine the average velocity for the particle as it moves from point A to point B. -1.0 m/s

  10. x(m) 3 2 1 0 A -1 B -2 -3 0 0.1 0.2 0.3 0.4 0.5 t(s) • Sample problem: From the graph, determine the average speed for the particle as it moves from point A to point B. 1.0 m/s

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