2. Uniform Motion t = 0 t = 1 s t = 2 s t = 3 s t = 4 st = 5 st = 6 s t = 7 s t = 8 s t (s)x (cm)v (cm/s) 00.0 1.05.05 2.010.05 3.015.05 4.020.05 5.025.05 6.030.05 7.035.05 8.040.05

3. Non-uniform motion t = 0 t = 1 s t = 2 s t = 3 s t = 4 st = 5 s t = 6 s t = 7 s t = 8 s t = 9 s

4. What is the velocity at t = 5.5 s? All we know from the given data is the average velocity between t = 5.0 and t = 6.0 s. Measure the object’s position at a smaller time interval, like t = 5.4 s and t = 5.6 s. Better yet, use t = 5.49 s and t = 5.51 s. The velocity at the instant t = 5.5 s is approximately equal to the average velocity during a small time interval from t = 5.49 s to t = 5.51 s. But the best we can do with the given data is guess. Chapter 2 Motion in 1-D PHY211 Dr. Aaron Titus t = 0 t = 1 s t = 2 s t = 3 s t = 4 st = 5 s t = 6 s t = 7 s t = 8 s t = 9 s

5. Instantaneous Velocity The velocity at an instant of time is called instantaneous velocity. It is approximately equal to the average velocity measured during a very small time interval.

6. Position vs. time graph t (s)x (cm) 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

7. Position vs. time graph t (s)x (cm) 00.0 1.00.5 2.02.2 3.05.0 4.08.8 5.013.8 6.019.9 7.027.2 8.035.4 9.045

8. Position vs. time graph -Slope of a tangent line on an x vs. t graph is instantaneous velocity. -Sign of slope (pos or neg) is direction of motion. -How slope changes tells you whether it is speeding up or slowing down.

9. Example Describe the motion of the object whose x vs. t graph is shown below.

10. Example Describe the motion of the object whose x vs. t graph is shown below.

11. Velocity vs. time graph t (s)x (cm)v (cm/s) 00.0 1.00.5 2.02.21.8 3.05.02.8 4.08.83.8 5.013.85.0 6.019.96.1 7.027.27.3 8.035.48.2 9.0459.6

12. Velocity vs. time graph t (s)x (cm)v (cm/s) 00.0 1.00.5 2.02.21.8 3.05.02.8 4.08.83.8 5.013.85.0 6.019.96.1 7.027.27.3 8.035.48.2 9.0459.6

13. Velocity vs. time graph -Slope of v vs. t graph is acceleration. -acceleration is the rate that the object speeds up or slows down. -if slope is constant, then the motion is characterized by constant acceleration

14. Example Describe the motion of the object whose v vs. t graph is shown below.

15. Example Describe the motion of the object whose v vs. t graph is shown below.

16. Example Describe the motion of the object whose v vs. t graph is shown below.

17. Observations If the object’s velocity is positive and the object speeds up, its acceleration is: 1.positive 2.negative 3.zero

18. Observations If the object’s velocity is positive and the object slows down, its acceleration is: 1.positive 2.negative 3.zero

19. Observations If the object’s velocity is negative and the object slows down, its acceleration is: 1.positive 2.negative 3.zero

20. Observations If the object’s velocity is positive and the object speeds up, its acceleration is: 1.positive 2.negative 3.zero

21. Matching position and velocity graphs 1.Note what is being plotted in a given graph. 2.Describe the motion in words or with a diagram. 3.Sketch (or match) the graph that matches the motion diagram or verbal description of the motion.

22. The graph at left shows a moving object’s velocity v vs clock reading t. One of the graphs below shows the object’s position x plotted vs t over the same time interval. Which one is it? v t 0 t t t t t ABC DE 00 0 0 0 x xx x x