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Kinematics

Kinematics. Kinematics is the study of motion Base of all subsequent physics Only directly measurable field of physics Can only measure displacements in space or time. Frames of Reference. In order to quantify any measurement, a Frame of Reference must be defined.

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Kinematics

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  1. Kinematics • Kinematics is the study of motion • Base of all subsequent physics • Only directly measurable field of physics • Can only measure displacements in space or time

  2. Frames of Reference • In order to quantify any measurement, a Frame of Reference must be defined. • Frames of reference use coordinate axes to quantify measurements • Coordinate axes are just number lines! • Number of orthogonal axes = number of dimensions

  3. Definition of Position • Position: Where an object is located. • Usually measured relative to the origin, but not necessary • Includes direction along the axis. • Displacement is how far an object is from a reference point • Includes direction along the axis.

  4. Example: Let an object be located at x = 4 m. Relative to the point x0 = 1 m, the displacement isDx = x – x0 = 4 m – 1 m = 3 m.Let another object be located at x’ = -5 m. The displacement to this point isDx’ = x’ – x0 = -5 m – 1 m = -6 m.

  5. Definition of Velocity • Velocity: The rate at which the position of an object changes. • Think of as how fast an object is moving. • Includes direction along the axis • Arrow reminds us to think about direction • This definition is the average velocity • Uses ending & starting position and time • Doesn’t take into account what happens in between • Speed: Magnitude of velocity • No directional information

  6. Definition of Acceleration • Acceleration: The rate at which the velocity of an object changes • Includes direction along axis • Tells how velocity changes; does not address velocity itself.

  7. Equations of motion • Assume initial time is zero, initial position, x0, is position at t = 0, and initial velocity, v0, is velocity at t = 0. • Assume final position and velocity are functions of time, x = x(t) and v = v(t), respectively. • Assume acceleration is constant • Start with definition of acceleration

  8. If the velocity is constant (a = 0), then the definition of velocity can be rearranged as • If acceleration is not zero, then v above is average velocity, vave.

  9. Know initial and final velocities, so average is • Substitute into previous equation

  10. Substituting equation of velocity yields

  11. If the time is not known, can use previous two equations to eliminate it • First solve velocity equation for time, t, • Substitute this into position equation

  12. Summary of equations

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