Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically...
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Transcript of Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically...
![Page 1: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/1.jpg)
Motion in Two and Three Dimensions
![Page 2: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/2.jpg)
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.
![Page 3: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/3.jpg)
The position vector for a particle is the vector sum of its vector components.
![Page 4: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/4.jpg)
In unit vector notation can be written as:
![Page 5: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/5.jpg)
The coefficients x, y, and z are the scalar components.
![Page 6: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/6.jpg)
The coefficients x, y, and z give the particle’s location along the coordinate axes and relative to the origin.
![Page 7: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/7.jpg)
The figure shows a particle with position vector:
![Page 8: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/8.jpg)
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).
![Page 9: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/9.jpg)
![Page 10: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/10.jpg)
If the position vector changes from during a certain time interval, then the particle’s displacement during that time interval is:
![Page 11: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/11.jpg)
We can rewrite this displacement as:
![Page 12: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/12.jpg)
Sample Problem 4-1
![Page 13: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/13.jpg)
Sample Problem 4-1
In figure 4-2 the position vector for a particle is initially
and then later it is
![Page 14: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/14.jpg)
What is the particle’s displacement from ?
![Page 15: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/15.jpg)
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
![Page 16: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/16.jpg)
At t = 15 seconds, what is the rabbit’s position vector in unit-vector notation and as a magnitude and an angle?
![Page 17: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/17.jpg)
Graph the rabbit’s path for t = 0 to t = 25 s.
![Page 18: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/18.jpg)
![Page 19: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/19.jpg)
Average Velocity and Instantaneous Velocity
If a particle moves through a displacement in time interval t, then its average
velocity is:
![Page 20: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/20.jpg)
Written as vector components:
![Page 21: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/21.jpg)
The instantaneous velocity is the value that approaches in the limit as t shrinks to
0.
![Page 22: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/22.jpg)
The direction of the instantaneous velocity of a particle is always tangent to the particle’s path at the particle’s position.
![Page 23: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/23.jpg)
The velocity of a particle along with the scalar components of
![Page 24: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/24.jpg)
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.
![Page 25: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/25.jpg)
![Page 26: Motion in Two and Three Dimensions. 4-2 Position and Displacement The position vector is typically used to indicate the location of a particle. The position.](https://reader033.fdocuments.in/reader033/viewer/2022051009/5a4d1b7b7f8b9ab0599b90c8/html5/thumbnails/26.jpg)
Average Acceleration and Instantaneous
Acceleration
When a particle’s velocity changes from to
in a time interval t, its average acceleration a avg during t is: