1. Physics Chapter 5

2. Position-Time Graph  Time is always on the x axis  The slope is speed or velocity Time (s) Position (m) Slope = Δ y Δ x

3. Velocity-Time Graph  Time is always on the x axis  The slope is acceleration  Area under the curve is position Slope = Δ y Δ x time (s) Velocity (m/s)

4. Area under velocity time graph is position Time (s) Velocity (m/s) Area = ½ b * h For this triangle A = ½ (velocity) (time)

5. Acceleration -Time Graph  Time is always on the x axis  Area under the curve is velocity time (s) Acceleration (m/s/s) Slope = Δ y Δ x

6. Area under acceleration time graph is velocity Time (s) Acceleration (m/s/s) Area = ½ b * h For this triangle A = ½ (acceleration) (time)

7. Acceleration is often graphed like this time (s) Acceleration (m/s/s) l+

8. Which makes area under the curve … time (s) Acceleration (m/s/s) l+ Area = b * h For this A = (acc) (time)

9. Looking at graphs  Average uses slope of the chord  Instantaneous uses slope of the tangent  If slope of the chord = slope of the tangent line then average = instantaneous

10. Average Velocity Which leads to a Kinematic Equation

11. Let time at 0 be 0 or

12. Position with Constant Velocity

13. Average acceleration Which leads to another Kinematic Equation

14. or Let time at 0 be 0

15. Final position with Constant acceleration

16. Time (s) Velocity (m/s) d = v 0 * t v0v0v0v0 v t d = ½ (v – v 0 ) * t or d = ½ vt – ½v 0 t Add them together & you get If the initial position is not zero, then add d 0 to the total distance

17. Final position with Constant acceleration

18. If v is not known, substitute the following equation in for v This leads to…

19. Final velocity with Constant acceleration Or simply

20. Final velocity with Constant acceleration Or simply

21. To solve this equation, note that it does not include time. Solve for t Sub t into:

22. Kinematic Equations