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Unit 1 A Kinematics

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Dynamics The branch of physics involving the motion of an object and the relationship between that motion and other physics concepts The branch of physics involving the motion of an object and the relationship between that motion and other physics concepts Kinematics is a part of dynamics Kinematics is a part of dynamics In kinematics, you are interested in the description of motion In kinematics, you are interested in the description of motion Not concerned with the cause of the motion Not concerned with the cause of the motion

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Brief History of Motion Sumaria and Egypt Sumaria and Egypt Mainly motion of heavenly bodies Mainly motion of heavenly bodies Greeks Greeks Also to understand the motion of heavenly bodies Also to understand the motion of heavenly bodies Systematic and detailed studies Systematic and detailed studies

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“Modern” Ideas of Motion Galileo Galileo Made astronomical observations with a telescope Made astronomical observations with a telescope Experimental evidence for description of motion Experimental evidence for description of motion Quantitative study of motion Quantitative study of motion

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Position Defined in terms of a frame of reference Defined in terms of a frame of reference One dimensional, so generally the x- or y- axis One dimensional, so generally the x- or y- axis

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Vector Quantities Vector quantities need both magnitude (size) and direction to completely describe them Vector quantities need both magnitude (size) and direction to completely describe them Represented by an arrow, the length of the arrow is proportional to the magnitude of the vector Represented by an arrow, the length of the arrow is proportional to the magnitude of the vector Head of the arrow represents the direction Head of the arrow represents the direction Generally printed in bold face type Generally printed in bold face type

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Scalar Quantities Scalar quantities are completely described by magnitude only Scalar quantities are completely described by magnitude only

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Displacement Measures the change in position Measures the change in position Represented as x (if horizontal) or y (if vertical) Represented as x (if horizontal) or y (if vertical) Vector quantity Vector quantity + or - is generally sufficient to indicate direction for one-dimensional motion + or - is generally sufficient to indicate direction for one-dimensional motion Units are meters (m) in SI, centimeters (cm) in cgs or feet (ft) in US Customary Units are meters (m) in SI, centimeters (cm) in cgs or feet (ft) in US Customary

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Displacements

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Distance Distance may be, but is not necessarily, the magnitude of the displacement Blue line shows the distance Red line shows the displacement

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Velocity It takes time for an object to undergo a displacement It takes time for an object to undergo a displacement The average velocity is rate at which the displacement occurs The average velocity is rate at which the displacement occurs generally use a time interval, so let t o =0 generally use a time interval, so let t o =0

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Velocity continued Direction will be the same as the direction of the displacement (time interval is always positive) Direction will be the same as the direction of the displacement (time interval is always positive) + or - is sufficient + or - is sufficient Units of velocity are m/s (SI), cm/s (cgs) or ft/s (US Cust.) Units of velocity are m/s (SI), cm/s (cgs) or ft/s (US Cust.) Other units may be given in a problem, but generally will need to be converted to these Other units may be given in a problem, but generally will need to be converted to these

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Speed Speed is a scalar quantity Speed is a scalar quantity same units as velocity same units as velocity total distance / total time total distance / total time May be, but is not necessarily, the magnitude of the velocity May be, but is not necessarily, the magnitude of the velocity

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Instantaneous Velocity The limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero The limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero The instantaneous velocity indicates what is happening at every point of time The instantaneous velocity indicates what is happening at every point of time

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Uniform Velocity Uniform velocity is constant velocity Uniform velocity is constant velocity The instantaneous velocities are always the same The instantaneous velocities are always the same All the instantaneous velocities will also equal the average velocity All the instantaneous velocities will also equal the average velocity

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Graphical Interpretation of Velocity Velocity can be determined from a position- time graph Velocity can be determined from a position- time graph Average velocity equals the slope of the line joining the initial and final positions Average velocity equals the slope of the line joining the initial and final positions Instantaneous velocity is the slope of the tangent to the curve at the time of interest Instantaneous velocity is the slope of the tangent to the curve at the time of interest The instantaneous speed is the magnitude of the instantaneous velocity The instantaneous speed is the magnitude of the instantaneous velocity

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Average Velocity

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Instantaneous Velocity

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Acceleration Changing velocity (non-uniform) means an acceleration is present Changing velocity (non-uniform) means an acceleration is present Acceleration is the rate of change of the velocity Acceleration is the rate of change of the velocity Units are m/s² (SI), cm/s² (cgs), and ft/s² (US Cust) Units are m/s² (SI), cm/s² (cgs), and ft/s² (US Cust)

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Average Acceleration Vector quantity Vector quantity When the sign of the velocity and the acceleration are the same (either positive or negative), then the speed is increasing When the sign of the velocity and the acceleration are the same (either positive or negative), then the speed is increasing When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing

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Instantaneous and Uniform Acceleration The limit of the average acceleration as the time interval goes to zero The limit of the average acceleration as the time interval goes to zero When the instantaneous accelerations are always the same, the acceleration will be uniform When the instantaneous accelerations are always the same, the acceleration will be uniform The instantaneous accelerations will all be equal to the average acceleration The instantaneous accelerations will all be equal to the average acceleration

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Graphical Interpretation of Acceleration Average acceleration is the slope of the line connecting the initial and final velocities on a velocity-time graph Average acceleration is the slope of the line connecting the initial and final velocities on a velocity-time graph Instantaneous acceleration is the slope of the tangent to the curve of the velocity-time graph Instantaneous acceleration is the slope of the tangent to the curve of the velocity-time graph

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Average Acceleration

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