kinematics position 1 z x y the location of a particle with respect to a spatial coordinate origin....
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KinematicsPosition
1
z
x
y
The location of a particle with respect to a spatial coordinate origin.
Position r
ˆ ˆ ˆ i j kr x y z zx
y
KinematicsPosition
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x
y
z
A measure of the change in position.
Displacement r
ˆ ˆ ˆ i j kr x y z
KinematicsPosition
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x
y
z
A measure of the length of the path (trajectory) traveled by the particle.
Distance s
s
KinematicsPosition
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It is POSITION (NOT DISTANCE) that is most important to a physicist!
So how do we define position for a physics problem?
Here are some rules of thumb to follow…
1. Each particle (object) in a problem should have its own set of positions associated with each time in the problem.a. We can label these with an informative subscript or
superscript. (e.g. or )b. Some objects will actually use the same position like when Dr.
Mike is sitting in the green car. In this case we can give them the same name using either or but not both.
Dr. Miker
green carr
Dr. Miker
green carr
KinematicsPosition
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It is POSITION (NOT DISTANCE) that is most important to a physicist!
So how do we define position for a physics problem?
Here are some rules of thumb to follow…
2. To define a position we need to determine the origin of a coordinate system.a. The location of the origin is either part of the problem (e.g.
measure the position from Dr. Mike) or it is a decision you have to make (making the decision wisely can make a problem easier to solve).
KinematicsPosition
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It is POSITION (NOT DISTANCE) that is most important to a physicist!
So how do we define position for a physics problem?
Here are some rules of thumb to follow…
3. To define a position we need to determine the direction of the axes.a. The direction of the axes is either part of the problem or it is a
decision you have to make (making the decision wisely can make a problem easier to solve).
b. The default is to make the x-axis point to the right, the y-axis point up and the z-axis point toward you.
Note this 45o line is used to represent a line point toward you.
x
y
z
KinematicsPosition
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It is POSITION (NOT DISTANCE) that is most important to a physicist!
So how do we define position for a physics problem?
Here are some rules of thumb to follow…
4. The position of an object is given by the vector .
5. The position requires THREE numbers to define it. These are the three components (x, y and z).
6. It is best to create a table with vector positions and components to help organize our thoughts.
r
Position x y zVariable Value Variable Value Variable Value
Dr. Miker
Dr. Mikex Dr. Mikey Dr. Mikez20 m 0 m
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Here are some examples.
Example #1
Given the problem…
Dr. Mike leaves for school in his Toyota Corolla at 10:00am. Bailey D. Wonderdog follows him exactly 50 minutes later. Dr. Mike (being a safe driver) drives 5 mph below the speed limit (65 mph to be exact); whereas, Bailey (being a superhero) has the need for speed and drives at 70 mph. How long will it take for Bailey to catch up with Dr. Mike?
What are the positions we must take into account?
Your answers
KinematicsPosition
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Here are some examples.
Example #2
Given the problem…
A ball is dropped from a cliff. The cliff’s height is 20 m. The ball falls under the influence of gravity only (free-fall). When it reaches the bottom, it bounces three times before rolling to a stop. How fast is it going just before it reaches the ground after falling from the cliff?
What are the positions we must take into account?
Your answers