Describing Motion

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

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

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

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

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

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

8. Velocity Units distance = m/s time

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

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

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

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

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

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

15. 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.

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

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

18. 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.

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

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

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