Assigned Groups

1. Assigned Groups • Find which group you’re in • Find where it is • Sit there • Be friendly 7 8 4 5 6 1 2 3 screen screen

2. Announcements • Show your name tags! • Please give Moodle your registered name • Labsanddiscussionshavealreadystarted

3. Standard • Relate distance, velocity, and acceleration mathematically, graphically, and conceptually. Objectives • Relate distance, velocity, and acceleration. • Interpret distance-time, velocity-time, and acceleration-time plots.

4. Describing Motion It’s all math today

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

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

8. Group Work: Graph Describe the Tortoise-and-hare race using a position-time graph. • Same axes • One world-line for tortoise, another for hare • Indicate significant times and positions

9. Dd average speed = over entire interval Dt Dd instantaneous speed = lim at one instant Dt t 0 Speed Rate of changing position

10. Speed as Slope D distance Speed = = slope of graph! D time distance Dd Dt time

11. Question Who had the highest average speed? • The tortoise. • The hare. • Their average speeds were the same. • Over what time interval?

12. Poll Question Who had the highest instantaneous speed? • The tortoise. • The hare. • Their instantaneousspeeds were the same. • At what time?

13. Speed Units distance = m/s time

14. Group Work: Graph Describe the Tortoise-and-hare race using a velocity-time graph.

15. hare tortoise Distance Change as Area • What are the areas under the tortoise’s and hare’s velocity-time plots? area = vDt = D(distance) speed t0 t1 t2 t3 t4 time

16. Group Work: Graph 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 velocity-time graph.

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

18. velocity m/s s time Acceleration Units = = m/s2

19. Group Work: Graph What is the car’s acceleration at the different times? Describe the car’s motion using an acceleration-time graph.

20. Group Work: Compute How far does the car travel: • Between 0 s and 5 s? • Between 10 s and 15 s?

21. slope = velocity d t slope = acceleration v area = distance t a area = velocity t Acceleration Starting from a traffic light that turns green

22. Group Work 7 Describe four ways (x-t, v-t, a-t, words): position 0 time

23. Group Work 7 Describe four ways (x-t, v-t, a-t, words): velocity 0 time

24. Group Work 7 Describe four ways (x-t, v-t, a-t, words): acceleration 0 time

25. Group Work 7 A coconut hangs motionless from its tree, then drops with increasing downward speed until it lands on the ground, quickly coming to rest. Describe four ways (x-t, v-t, a-t, words):

26. Formulas for Constant Acceleration • Velocity change Dv=aDt • Velocity vt = v0 + Dv = v0 + aDt • Position change Dx = v0 Dt + 1/2 a (Dt)2 • Position xt = x0 + v0 Dt + 1/2 a (Dt)2

27. Reading for Next Time • Vectors: how we handle quantities with directions • Important vectors: position, velocity, acceleration, force