SPH3U1 Lesson 03 Kinematics
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1 SPH3U1 Lesson 03 Kinemaics GRAPHICAL ANALYSIS LEARNING GOALS Sudens will Learn how o read values, find slopes and calculae areas on graphs. Learn wha hese values mean on boh posiion-ime and velociy-ime graphs. INTERPRETING VELOCITY-TIME GRAPHS Examine each Velociy-Time Graph and deermine he direcion he objec is moving, wheher he velociy consan or changing and wheher he acceleraion is posiive or negaive. Direcion of velociy Velociy is Value of acceleraion is Direcion of velociy Velociy is Value of acceleraion is Direcion of velociy Direcion of acceleraion is Velociy is (increasing,decreasing) Direcion of velociy above axis Direcion of velociy below axis Wha happened a crossing of axis? Direcion of acceleraion is Velociy above axis is Velociy below axis is 1
2 Posiion (m [E]) Posiion (m [E]) SPH3U1 Lesson 03 Kinemaics Direcion of velociy Direcion of acceleraion is Velociy is (increasing,decreasing) Direcion of velociy above axis Direcion of velociy below axis Wha happened a crossing of axis? Direcion of acceleraion is Velociy above axis is Velociy below axis is THREE STEPS TO GRAPHICAL ANALYSIS POSITION-TIME GRAPHS 1. You can read values off he graph. 2. You can find slope(s) of he graph (angen = insananeous, secan = average). 3. You can calculae he area beween he curve and he x-axis of he graph. Posiions can be read off he graph. Displacemens are a change in posiion. Read he iniial and final posiion and subrac. Average velociy over an inerval is he slope of he line joining he end-poins of he inerval (he secan). Insananeous velociy a a poin is slope of he angen a ha poin. When he curve is a parabola, he insananeous velociy a he cenre of an inerval is equal o he average velociy of he enire inerval. Insananeous Velociy 4 Posiion vs Time Average Velociy 4 Posiion vs Time 3 2 Run ( ) Rise ( ) 3 2 Run ( ) Rise ( ) VELOCITY-TIME GRAPHS Are graphs of insananeous velociy ploed agains ime. Insananeous velociies can be read from he graph. Average acceleraion over an inerval is deermined by he slope of he line joining he wo poins (he secan). Insananeous acceleraion a a poin is he slope of he angen a ha poin. When he velociy and he acceleraion have he same sign, he objec is speeding up (he line goes away from he ime axis). When he velociy and he acceleraion have he opposie sign, he objec is slowing down (he line approaches he ime axis). 2
3 Velociy (m/s [E]) Velociy (m/s [E]) SPH3U1 Lesson 03 Kinemaics The displacemen during an inerval can be found from he area beween he curve and he ime axis over ha inerval. o Areas above he axis are posiive and areas below he axis are negaive. Average velociies are found from he definiion of average velociy: displacemen over ime. Average Acceleraion 15.0 Velociy vs Time Rise ( ) 15.0 Velociy vs Time Displacemen area of coloured shapes under he graph. 5.0 Run ( ) POSITION-TIME TO VELOCITY-TIME GRAPHS You can use he informaion in a posiion-ime graph o creae a velociy-ime graph. Find he slope of each secion on he following posiion-ime graph. The secions are deermined by a change in slope and a change in he sign of he posiion. Make a able of your resuls below. Then use he able of values from your posiion-ime graph o plo a velociy ime graph. 3
4 SPH3U1 Lesson 03 Kinemaics VELOCITY-TIME TO POSITION-TIME GRAPHS You can use he informaion in a velociy-ime graph o draw a posiion-ime graph. To skech he posiion-ime graph, find he area under he velociy-ime graph for each secion. The secions are deermined by a change in slope or sign of he velociy. Make a able showing he TOTAL AREA FROM 0 up o each 5 s of ime. Then plo he daa on he posiion-ime graph. 4
5 Acceleraion (m/s 2 [N]) Velociy (m/s [N]) Posiion (m [N]) SPH3U1 Lesson 03 Kinemaics TRANSITION GRAPHS Draw he corresponding posiion-ime graph and acceleraion-ime graph for he velociy-ime graph shown. Show calculaions and ables of daa a he sides of all graphs. Posiion vs Time 20 Velociy vs Time Acceleraion vs Time 5
6 Acceleraion (m/s 2 [N]) Velociy (m/s [N]) Posiion (m [N]) SPH3U1 Lesson 03 Kinemaics Posiion vs Time Velociy vs Time Acceleraion vs Time 6
7 Acceleraion (m/s 2 [N]) Velociy (m/s [N]) Posiion (m [N]) SPH3U1 Lesson 03 Kinemaics Posiion vs Time 20 Velociy vs Time Acceleraion vs Time 7
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