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Kinematics gives us the tools to describe motion.
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Consider a point mass, the displacement of the point mass is the vector which points from its starting point
to its ending point . We denote the displacement as . -
Displacement can be a function of time
. Viewed in this way, the velocity is defined as And acceleration is defined as
Discrete variants of these also exist where we replace the differentials with approximations (i.e.
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The velocity is tangent to the point mass’ trajectory at every point.
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Speed is defined as the magnitude of velocity. Distance is defined as the magnitude of displacement.
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From the above definitions, we can define the four Kinematic Equations
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Acceleration can be redefined using bases that are parallel and perpendicular along its path of motion. This translates into a change in speed and turning, respectively.
- If a moving object is turning (changing direction),its acceleration vector points ahead of the normal to its path if it is speeding up
- Its acceleration points behind the normal if it is slowing down
- Its acceleration points along the normal if its speed is instantaneously not changing. \
Relativity
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Relativity is the phenomenon where two observers measure the velocity of the same object differently if one observer is moving relative to the other. Relative velocity is the velocity relative to a particular observer.
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Every observer is assumed to have a frame of reference - a coordinate system plus a time scale.
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The velocity of object
relative to is denoted as . If we have another observer , then we have that -
For two objects, the relative velocity is given by
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All of the above extends to any other quantity (i.e., position or acceleration)