1. © 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials. Lecture Powerpoints Physics for Scientists and Engineers, 3 rd edition Fishbane Gasiorowicz Thornton

2. Chapter 2 Straight-Line Motion

3. Main Points of Chapter 2 Displacement Speed and Velocity Acceleration Motion with Constant Acceleration Freely Falling Objects Integration and Motion in One Dimension

4. 2-1 Displacement Displacement is distance traveled: Similarly, time interval is defined as: (2-1) (2-2) Graph of distance vs. time in 100-m dash:

5. 2-1 Displacement Net displacement: straight-line distance between initial position and final position; for a round trip, net displacement is zero Displacement is a vector: points from initial position to final position Not an issue in one-dimensional motion, but becomes important in two- and three- dimensional motion

6. 2-2 Speed and Velocity Average speed is defined as total distance traveled / total time interval As time interval becomes shorter and shorter without limit, average speed becomes instantaneous speed: the rate at which distance changes with time

7. 2-2 Speed and Velocity General problem-solving techniques: Read the problem carefully Draw a sketch or diagram Write down known quantities Figure out what you need to solve for

8. 2-2 Speed and Velocity General problem-solving techniques (cont): Which physical principles link known quantities to unknown ones? Figure out what equations to use, and make sure they apply in this particular situation Solve equations algebraically, so you can check that your solution has the right dimensions Make sure your answer is reasonable!

9. 2-2 Speed and Velocity Velocity is a vector – points in the direction of motion at any particular instant (except average velocity, which is calculated from the total displacement and points from the initial to the final position)

10. 2-2 Speed and Velocity Instantaneous velocity: (2-9) (2-10)

11. 2-2 Speed and Velocity Instantaneous speed is magnitude of velocity In graph of position vs. time, instantaneous velocity is slope of line at each point:

12. 2-2 Speed and Velocity Position as a function of time: (2-12) Three possible, and one impossible, x vs. t graphs:

13. 2-3 Acceleration Acceleration is rate of change of velocity with time Average acceleration: (2-13) Instantaneous acceleration: (2-14)

14. 2-3 Acceleration Instantaneous acceleration is slope of velocity-vs.-time curve:

15. 2-3 Acceleration Relationship between acceleration and displacement: (2-15)

16. 2-4 Motion with Constant Acceleration Velocity with constant acceleration: (2-17) Average velocity: (2-18) Position as a function of time:

17. 2-4 Motion with Constant Acceleration For constant acceleration: (2-19) Substituting: (2-21) Further substitution to eliminate t gives: (2-24)

18. 2-5 Freely Falling Objects Acceleration due to gravity near Earth’s surface: Direction: towards center of Earth Equations of motion for freely falling objects: (2-26a,b,c,d)

19. 2-6 Integration and Motion in One Dimension If object’s position is known as a function of time, can take derivatives to find velocity and acceleration. What about the reverse? If we know the velocity and/or the acceleration as functions of time, can we find the displacement?

20. 2-6 Integration and Motion in One Dimension Displacement will be sum of areas under the curve in a v-t plot:

21. 2-6 Integration and Motion in One Dimension In the limit that the width of the segments becomes infinitesimally small, the sum becomes an integral: (2-29) (2-30)

22. 2-6 Integration and Motion in One Dimension Similarly, we can find the velocity from the acceleration: (2-32) If acceleration is constant, integrating to find the velocity and then the displacement gives the usual kinematic equations.

23. Summary of Chapter 2 Displacement in one dimension: (2-1) Instantaneous velocity: (2-10) Instantaneous acceleration: (2-14)

24. Summary of Chapter 2, cont. Equations of motion for constant acceleration: Freely falling objects obey the same equations, with the acceleration g due to gravity

25. Summary of Chapter 2, cont. Can integrate to find velocity and displacement from acceleration: