Calculate position vectors in a multidimensional displacement problem.
Solve for the displacement in two or three dimensions.
Calculate the velocity vector given the position vector as a function of time.
Calculate the average velocity in multiple dimensions.
Displacement and velocity in two or three dimensions are straightforward extensions of the one-dimensional definitions. However, now they are vector quantities, so calculations with them have to follow the rules of vector algebra, not scalar algebra.
Displacement vector
To describe motion in two and three dimensions, we must first establish a coordinate system and a convention for the axes. We generally use the coordinates
x ,
y , and
z to locate a particle at point
P (
x ,
y ,
z ) in three dimensions. If the particle is moving, the variables
x ,
y , and
z are functions of time (
t ):
[link] shows the coordinate system and the vector to point
P , where a particle could be located at a particular time
t . Note the orientation of the
x ,
y , and
z axes. This orientation is called a right-handed coordinate system (
Coordinate Systems and Components of a Vector ) and it is used throughout the chapter.
With our definition of the position of a particle in three-dimensional space, we can formulate the three-dimensional displacement.
[link] shows a particle at time
located at
with position vector
At a later time
the particle is located at
with position vector
. The
displacement vector
is found by subtracting
from
Vector addition is discussed in
Vectors . Note that this is the same operation we did in one dimension, but now the vectors are in three-dimensional space.
The following examples illustrate the concept of displacement in multiple dimensions.
Polar orbiting satellite
A satellite is in a circular polar orbit around Earth at an altitude of 400 km—meaning, it passes directly overhead at the North and South Poles. What is the magnitude and direction of the displacement vector from when it is directly over the North Pole to when it is at
latitude?
Strategy
We make a picture of the problem to visualize the solution graphically. This will aid in our understanding of the displacement. We then use unit vectors to solve for the displacement.
Solution
[link] shows the surface of Earth and a circle that represents the orbit of the satellite. Although satellites are moving in three-dimensional space, they follow trajectories of ellipses, which can be graphed in two dimensions. The position vectors are drawn from the center of Earth, which we take to be the origin of the coordinate system, with the
y -axis as north and the
x -axis as east. The vector between them is the displacement of the satellite. We take the radius of Earth as 6370 km, so the length of each position vector is 6770 km.
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
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_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life