1 / 26

Motion in Two and Three Dimensions: Position & Displacement

Learn about position vector, displacement, and velocity in both 2D and 3D motion, with examples and unit vector notation. Explore average and instantaneous velocity and acceleration concepts.

asharpe
Télécharger la présentation

Motion in Two and Three Dimensions: Position & Displacement

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Motion in Two and Three Dimensions

  2. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position vector is a vector that extends from a reference point (usually the origin) to the particle.

  3. The position vector for a particle is the vector sum of its vector components.

  4. In unit vector notation can be written as:

  5. The coefficients x, y, and z are the scalar components.

  6. The coefficients x, y, and z give the particle’s location along the coordinate axes and relative to the origin.

  7. The figure shows a particle with position vector:

  8. As a particle moves, its position vector changes in such a way that the position vector always extends to the particle from the reference point (origin).

  9. If the position vector changes from during a certain time interval, then the particle’s displacement during that time interval is:

  10. We can rewrite this displacement as:

  11. Sample Problem 4-1

  12. Sample Problem 4-1 In figure 4-2 the position vector for a particle is initially and then later it is

  13. What is the particle’s displacement from ?

  14. Sample Problem 4-2 A rabbit runs across a parking lot on which a set of coordinate axes has been drawn. The coordinates of the rabbit’s position as functions of time t are given by: x = -0.3t2 + 7.2t + 28 y = 0.22t2 - 9.1t + 30

  15. At t = 15 seconds, what is the rabbit’s position vector in unit-vector notation and as a magnitude and an angle?

  16. Graph the rabbit’s path for t = 0 to t = 25 s.

  17. Average Velocity and Instantaneous Velocity If a particle moves through a displacement in time interval D t, then its average velocity is:

  18. Written as vector components:

  19. The instantaneous velocity is the value that approaches in the limit as Dt shrinks to 0.

  20. The direction of the instantaneous velocity of a particle is always tangent to the particle’s path at the particle’s position.

  21. The velocity of a particle along with the scalar components of

  22. Sample Problem 4-3 For the rabbit in sample problem 4-2, find the velocity at time t = 15 s, in unit vector notation and as a magnitude and an angle.

  23. Average Acceleration and Instantaneous Acceleration When a particle’s velocity changes from to in a time interval Dt, its average acceleration a avg during Dt is:

More Related