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Kinematics Kinematics is the branch of physics that describes the motion of points, bodies (objects) and systems of bodies (groups of objects) without consideration of the causes of motion.

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Kinematics One-dimensional kinematics involves movement along one axis. We set up a one dimensional coordinate system with an x axis and the origin at x=0 Position – the position in our coordinate system is the value of x.

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Figure 2-1 A One-Dimensional Coordinate System

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Kinematics Distance – the total length of travel. It always has a positive value. It is a scalar quantity – completely characterized only by magnitude. SI unit: meter

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Kinematics Displacement – the change in position Δx. It is a vector quantity completely characterized by magnitude and direction. Δx=x f -x i SI unit: meter, m Δx can be positive, negative or zero.

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Kinematics Average speed – distance divided by elapsed time. Average velocity – displacement divided by elapsed time. SI unit for speed and velocity:

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Kinematics Instantaneous speed – the magnitude of velocity at a given instant. Instantaneous velocity – the velocity at a given instant.

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Kinematics Average acceleration – the change in velocity divided by the change in time.

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Kinematics Instantaneous acceleration – the acceleration at a given instant.

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Kinematics Constant acceleration – when acceleration is constant, instantaneous acceleration is equal to the average acceleration. In this course we will only be dealing with situations involving constant acceleration (with one exception).

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Kinematics In the following slide quantities with the subscript 0 refers to the value of a quantity at the beginning of an event, and the quantities without a subscript refers to the value of a quantity at the end of an event. Δt becomes t if t 0 =0 Frequently the quantities with the subscript 0 equal zero, and drop out from the equations.

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Table 2-4 Constant-Acceleration Equations of Motion Variables RelatedEquationNumber Velocity, time, acceleration v = v 0 + at2-7 Initial, final, and average velocity v av = ½(v 0 + v)2-9 Position, time, velocity x = x 0 + ½(v 0 + v)t2-10 Position, time, acceleration x = x 0 + v 0 t + ½ at 2 2-11 Velocity, position, acceleration v 2 = v 0 2 + 2a(x – x 0 ) = v 0 2 + 2a x 2-12

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