1. SCI340 L03_dva Position, velocity, and acceleration
Describing Motion
Position, velocity, and acceleration
§2.1–2.4

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

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

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

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

7. Poll Question Who had the fastest average speed? The tortoise.
The hare.
Their average speeds were the same.
Over what time interval?

8. Speed Units
distance
= m/s
time

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

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

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

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

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

14. Speeds and Areas speed area = vDt = D(distance) time hare tortoise t0

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

17. Poll Question What is the SI unit for acceleration? m. s. m·s. m/s.

18. Group 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
time

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

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