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Motion

Motion. Displacement. Consider the motion of a point that is constrained to move in a straight line. .

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Motion

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  1. Motion

  2. Displacement Considerthemotion of a pointthatisconstrained to move in a straight line. Todistinguishthetwopointswe introduce the concept of displacement. Thedisplacement of a pointfrom O willbe a quantitywhosenumericalvaluewillbethedistance and itssignwilltellusifthepointistotherightorleft of O.

  3. Displacement Wewill use the symbol xfordisplacement in a straight line and s fordistance. Displacement, being a vector isrepresentedgraphicallybyanarrowthatbegins at O and ends at thepoint of interest. Wewill use the capital letterSto stand forthe total distancetravelled, and Δxforthechange in displacement. Thechange in displacementisdefinedby Δx = final displacement – initialdisplacement

  4. Examplequestions

  5. Speed Ifanobjectcovers a total distanceS in a total time T, theaveragespeed of theobjectsisdefinedby

  6. Velocity Averagespeedis a positive quantitythatdoesnottakeintoaccountthedirection in whichtheobjectmoves. To do thatwe introduce the concept of velocity. Theaveragevelocityfor a motionisdefined as thechange in displacement of theobjectdividedbythe total time taken.

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  8. Uniformmotion Motionwithuniformvelocitymeansmotion in whichthevelocityisconstant. Thisimpliesthatthedisplacementchangesbyequalamounts in equalintervals of time (no matterhowsmallorlarge). Letustaketheinterval o time fromt = 0 to time t. Ifthedisplacement at t = 0 isx0and thedisplacement at time tisx, thenitfollowsthat v = Δx/Δt = (x-x0)/(t-t0) x = x0 + vt

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  10. Frames of reference Thereis no absolutemeaningtothestatement ‘being at rest’. No experiment can be performedtheresult of whichwill be toletobserversknowthatthey are movingwithconstantvelocity and thatthey are not at rest. Anobserverwho uses measuring tapes and stopwatchesto observe and record motioniscalled a frame of reference.

  11. Relativevelocity This introduces the concept of relativevelocity. Lettwoobservers P and Q havevelocitiesvP and vQ as measuredbythesameframe of reference. Thentherelativevelocity of P withrespectto Q issimply

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  13. Graphsforuniformmotion

  14. Graphsforuniformmotion

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  16. …more questions

  17. Acceleration Totreatsituations in whichvelocityisnotconstantweneedto define accelerationa. IfthevelocitychangesbyΔv in a very short interval of time Δtthen a = Δv/Δt isthedefinition of theinstantaneousacceleration. Whenaccelerationisconstant, themotioniscalleduniformlyacceleratedmotion.

  18. Acceleration Formotion in a straight line, positiveaccelerationmeansthatthevelocityisincreasingwhereasnegativeaccelerationimplies a decreasingvelocity.

  19. Accelerationduetogravity Whenanobjectisdroppedorthrown, thereisanaccelerationthatactsonallobjects and has thesamemagnitudeforallbodiesindependently of theirmass. Onearththemagnitude of thisaccelerationisabout 9.8 m/s2.

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  21. Graphsforuniformlyacceleratedmotion

  22. Displacement Even in the case of acceleratedmotion, thechange in displacementistheareaunderthevelocity-time graph.

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  24. Graphs of acceleration versus time In a graph of acceleration versus time theareaunderthegraphgivesthechange in velocitiy.

  25. Graphs of displacement versus time In motionwithconstantacceleration, a graph of displacement versus time is a parabola. Drawingthetangent at a pointonthe curve and findingtheslope of thetangentgivesthevelocity at thatpoint.

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