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Understanding Acceleration in Velocity-Time Graphs

Explore acceleration in velocity-time graphs through examples and problems. Learn about positive, negative, and zero acceleration scenarios and how to calculate average acceleration. Practice with homework problems included.

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Understanding Acceleration in Velocity-Time Graphs

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  1. Journal #12 • If the trend continues, where would the object be at 10 seconds?

  2. Chapter 3.1 • Acceleration

  3. Velocity-time Graphs • A graph that plots an object’s velocity versus the time. • The rate at which an object’s velocity is changing is called acceleration and can be found by calculating the slope of the velocity-time graph.

  4. Example Graph:

  5. Facts about acceleration: • Acceleration is the change in velocity divided by the time it takes to make that change. • It is possible to have positive or negative acceleration as well as acceleration equal to zero. • Acceleration is a vector quantity with the SI unit of m/s2, pronounced “meters per second squared.” • A change in direction will cause a change in acceleration.

  6. pos Velocity (m/s) 0 Time (s) neg Acceleration Possibilities (there are 9)

  7. If initial velocity is zero… 3 possibilites • vi= 0 and a = 0: • The object is at rest and remains at rest • vi= 0 and a = positive: • The object is at rest and begins to move forward with increasing speed. • vi= 0 and a = negative: • The object is at rest and begins to move backward with increasing speed.

  8. If initial velocity is positive… 3 possibilities • vi= positive and a = negative: • The object is moving in a forward direction and is decreasing speed. • vi= positive and a = 0: • The object is moving in a forward direction at a constant speed. • vi= positive and a = positive: • The object is moving in a forward direction and is increasing speed.

  9. If initial velocity is negative… 3 possibilites • vi= negative and a = negative: • The object is moving in a backward direction and is increasing speed. • vi= negative and a = 0: • The object is moving in a backward direction at a constant speed. • vi= negative and a = positive: • The object is moving in a backward direction and is decreasing speed.

  10. Calculating Average Acceleration This formula is cannot fit into any “magic triangle”, so we have to learn it the regular way.

  11. Example Problem 1 • Describe the motion of the object represented in this graph:

  12. From 0 to 5.0 s: • Speeds up from rest at a constant rate • From 5.0 to 10.0s: • Remains at a constant speed of 30.0m/s • From 10.0 to 15.0s: • Decreases in speed from 30 to 20m/s • From 15.0 to 20.0s: • Remains at a constant speed of 20m/s • From 20.0 to 25.0s: • Comes to a stop

  13. Example Problem 2 • Find the uniform acceleration that causes a car’s velocity to change from 32 m/s to 96 m/s in an 8.0-s period.

  14. Ex Prob 2 picture t = 8.0s a = ? Notice how every number in the problem is represented in the picture! vi = 32m/s vf = 96m/s

  15. Ex Prob 2 work Fill in the left-hand line up! • a = • vf = • vi = • t =

  16. Ex Prob 2 work • a = ? • vf = 96 m/s • vi = 32 m/s • t = 8.0s

  17. Example Problem 3 • A car with a velocity of 22 m/s is accelerated uniformly at the rate of 1.6 m/s2 for 6.8 s. What is its final velocity?

  18. Ex Prob 3 picture t = 6.8s a = 1.6m/s2 vi = 22m/s vf = ?

  19. Ex Prob 3 work Fill in the left-hand line up! • a = • vf = • vi = • t =

  20. Ex Prob 3 work • a = 1.6 m/s2 • vf = ? • vi = 22 m/s • t = 6.8 s

  21. Homework Problems • P. 61, #3 and 4 • P. 64, #6-10

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