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Describing Motion

Analyzing the Tortoise and Hare race using position-time, velocity-time, and acceleration-time graphs. Determine fastest average velocity and maximum instantaneous speed.

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Describing Motion

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  1. Describing Motion Position, velocity, and acceleration §2.1–2.4

  2. The Tortoise and the Hare Told in words, formulas, and graphs

  3. Board Work Describe the Tortoise-and-hare race using a position-time graph.

  4. Question Who was fastest? • The tortoise. • The hare. • They had the same speed. • What do you mean by faster?

  5. Dx average velocity = over entire interval Dt Velocity Rate of changing position

  6. Question Who had the fastest average velocity? • The tortoise. • The hare. • Their averagevelocities were the same. • Over what time interval?

  7. Velocity Units distance = m/s time

  8. Velocity as Slope D distance Velocity = = slope of graph! D time distance Dx Dt time

  9. lim Dt0 Instantaneous velocity smaller Dt finite Dt Young and Freedman, Figure 2.7

  10. Instantaneous Velocity Dx instantaneous velocity = lim at one instant Dt Dt 0

  11. Question Who had the fastest maximum instantaneous speed? • The tortoise. • The hare. • Their instantaneousspeeds were the same.

  12. Board Work Describe the Tortoise-and-hare race using a velocity-time graph.

  13. hare tortoise Speeds and Areas speed area = vDt = D(x) t0 t1 t2 t3 t4 time

  14. Board Work A car waits at a stop light for 5 seconds, smoothly accelerates to 15 m/s over 5 seconds, and then continues at 15 m/s. Describe the car’s motion using a speed-time graph.

  15. Dv average acceleration = Dt over the entire interval Dv instantaneous acceleration = lim Dt Dt 0 at one instant Acceleration Rate of changing velocity

  16. Question What is the SIunit for acceleration? • m. • s. • m·s. • m/s. • m2/s. • m/s2. • m2/s2.

  17. Group Board Work In the car scenario: What is the car’s acceleration during the different segments of its motion? Describe the car’s motion using an acceleration-time graph.

  18. Group Work Describe four ways (x-t, v-t, a-t, words): position 0 time

  19. Group Work Describe four ways (x-t, v-t, a-t, words): velocity 0 time

  20. Group Work Describe four ways (x-t, v-t, a-t, words): acceleration 0 time

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