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Acceleration

Acceleration. Physics Mrs. Coyle. Part I. Average Acceleration Instantaneous Acceleration Deceleration Uniform Accelerated Motion. Acceleration. The rate of change of velocity per unit time. It is a vector quantity. Simulation of Constant Velocity Compared to Constant Acceleration.

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Acceleration

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  1. Acceleration Physics Mrs. Coyle

  2. Part I • Average Acceleration • Instantaneous Acceleration • Deceleration • Uniform Accelerated Motion

  3. Acceleration • The rate of change of velocity per unit time. • It is a vector quantity.

  4. Simulation of Constant Velocity Compared to Constant Acceleration • http://higheredbcs.wiley.com/legacy/college/halliday/0471320005/simulations6e/index.htm?newwindow=true

  5. Average Acceleration Average Acceleration = Change in Velocity Time Interval a = Dv Dt a = v2- v1 t2 – t1

  6. Note: • Dv = final velocity – initial velocity

  7. Units of Acceleration • Examples of units of acceleration are: m/s2 or m/s/s km/h2 or km/h/h km/h/s

  8. Instantaneous Acceleration • Instantaneous Acceleration is the acceleration at a given instant. • Can you always tell if you are accelerating while observing the speedometer of a car?

  9. Questions: • If you are riding on a merry-go-round at a constant speed of 2m/s are you accelerating? • When you are riding in a car at a constant speed of 5mph turning right, are you accelerating?

  10. Signs of Acceleration • Acceleration is + when Dv > 0 • Acceleration is - when Dv < 0

  11. Deceleration • Deceleration is acceleration that causes the velocity’s magnitude to be reduced. • Is it necessary for deceleration to be negative?

  12. Uniform Accelerated Motion • Motion with constant acceleration • Straight line • Same direction

  13. Example 1: “The Bee” A bee is flying in the air with an initial velocity of +0.5m/s. It then accelerates for 2.0 s to a velocity of +1.5m/s. • Draw a motion diagram. • Draw a vector diagram showing the initial and final velocity and the acceleration of the bee. • Calculate the acceleration of the bee. Answer: +0.5m/s2

  14. Example 2 • The bee decides to slow down from +1.75m/s to +0.75m/s in 2s. • Draw the motion diagram. • Draw the vector diagram. • What was the acceleration of the bee? • Answer: -0.5m/s2

  15. Solving for vf : vf= vi+ a Δt vf= vi+ a t

  16. Example 3: • Susan slides on the icy sidewalk with an initial velocity of 2m/s. She slows down for 3s at 0.5m/s2. • Draw the vector diagram. • What is her final velocity? • Answer: 0.5m/s

  17. Part II Graphs of Accelerated Motion • Position-Time • Velocity-Time • Acceleration-Time

  18. Example 1: Position vs Time Parabola + Position (m) o Time (s) • What is the slope of the tangent to the curve at t=0s? • Is the slope of the tangent to the curve increasing or decreasing with increasing time?

  19. Note: • The slope of the tangent to the curve at a given time of the position-time graph is the instantaneous velocity.

  20. Velocity vs Time Velocity (m/s) + o Time (s) • Slope of Line= Acceleration • Area Under Line=Displacement (Change in Position)

  21. The slope of the line of the velocity- time graph is the instantaneous acceleration. • For constant acceleration that slope also equals the average acceleration. • For motion with varying acceleration, the velocity graph would be a curve. The slope of the tangent to the curve at a given time would represent the instantaneous acceleration.

  22. Acceleration vs Time Acceleration (m/s2) + o Time (s) Positive Acceleration

  23. Give a qualitative example of the previous motion.

  24. Example 2: Position vs Time Parabola + Position (m) o Time (s) 5s • What is the slope of the tangent to the curve at t=5s? • Is the slope to the tangent, positive or negative at t=0 s? • Is the slope of the tangent, increasing or decreasing with increasing time?

  25. Velocity vs Time Velocity (m/s) + o Time (s) • Is the slope of the line positive or negative?

  26. Acceleration vs Time Acceleration (m/s2) + o Time (s) • The acceleration is negative.

  27. Give a qualitative example of the previous motion?

  28. Note: • Area Under Line of the velocity-time graph =Displacement (Change in Position) • Area under the line of the acceleration-time graph =Change in Velocity

  29. Example: Calculate the displacement between 0 and 10 s v(m/s) 10m/s 5m/s o Time (s) 10s • Hint: Area Under the Line=Displacement Δd or simply d Answer: 75m

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