Wile Plus Assignmen 1 is online: 6 problems from chapers and 3 1D and D Kinemaics Due Monda Ocober 5 Before 11 pm!
Chaper II: Kinemaics In One Dimension Displacemen Speed and Veloci Acceleraion Equaions of Kinemaics for Consan Acceleraion Applicaions of he Equaions of Kinemaics Freel Falling Bodies Graphical Analsis of Veloci and Acceleraion
Graphical Analsis of Veloci and Acceleraion Aerage speed / 8/ 4 m/s The slope of he cure is consan, so he speed is consan. Sepember 9 3
4 1 m/s 4 m/s 4 4 3 1 m/s Sepember 9 4
Speed is no consan Insananeous speed a = s is (6 m)/(5 s) = 5. m/s Sepember 9 5
Consan Acceleraion Acceleraion = (1 m/s)/( s) = 6 m/s The slope of he cure is consan, so he acceleraion is consan Sepember 9 6
Eample: A person who walks for eercise produces he posiion-ime graph gien below. a) Wihou an calculaions, decide which segmen of he graph (A, B, C, or D) indicaes a negaie aerage eloci. B) decide which segmen indicaes a zero aerage eloci. Sepember 9 7
Eample: A bus makes a rip according o he posiion-ime graph shown below. Wha is he aerage acceleraion (in km/h ) of he bus for he enire 3.5 hour period? Sepember 9 8
Chaper 3 Kinemaics in Two Dimensions Equaions of Kinemaics in Two Dimensions Projecile Moion Displacemen, eloci, acceleraion eended o wo dimensions Moion in can be separaed compleel from moion in, proided air resisance is negligible reamen of projecile moion Sepember 9 9
Speed, Veloci and Acceleraion in One Dimension Disance o Aerage speed elapsed ime o Displacemen Aerage eloci elapsed ime o Insanane ous Veloci lim change ineloci Aerage acceleraion elapsed ime Insanane ous Accelerai on lim Sepember 9 1 o o
Speed, Veloci and Acceleraion In Two Dimensions Posiion ecors r, r a, Displacemen r r r r Aerage eloci o r Insanane ous Veloci lim o Aerage acceleraion o Insanane ous Accelerai on lim There is an acceleraion wheneer here is a change of speed or direcion! Sepember 9 11
Vecors can be resoled ino componens Insananeous eloci cos ˆ sin ˆ The componens separael follow he same equaions of moion as in he one dimensional case, since he moion for each componen happens in one dimension! Sepember 9 1
Sepember 9 13 a 1 a 1 o a Equaions of Kinemaics in Two Dimensions 1) ) 3) 4) a 1 a 1 o a Same as before, onl wih subscrips for each direcion of moion
Problem 3.8: A skaeboarder rolls down a 1 m ramp, reaching a speed of 7.7 m/s a he boom. Wha is her aerage acceleraion? If he ramp has an angle of 5 degrees wih respec o he horizonal, wha is he componen of acceleraion in he horizonal direcion? 1 m a ŷ ˆ 7. 7 m/s Sepember 9 14
a 1 m ŷ ˆ 7. 7 m/s Sepember 9 15
Eample: A spacecraf is raeling wih a eloci of = 548 m/s along he posiie direcion. Two engines are fired for 84 seconds. Engine 1 : Wha is he final speed in he and direcions? Wha is he oal final eloci? a Engine : a 1. m/s 8. 4 m/s Sepember 9 16
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Projecile Moion Consider moion in and separael Ignore air resisance eloci in -direcion is consan Wrie down posiions in and as a funcion of ime Remember ha he projecile raels ericall (up and down ) in he same ime ha i is raeling aboe he horizonal () The onl acceleraion is ha due o grai, acing downward (a rocke or an objec which is self propelled is no considered a projecile and does no undergo projecile moion, because i can be acceleraed arbiraril in an direcion.) Sepember 9 18
ŷ g is consan ˆ a a g ˆ m g 9. 8 ˆ s In he absence of air resisance: no forces ac in -direcion, so, he speed in -direcion is consan hroughou he pah. Speed changes in -direcion because of grai. Sepember 9 19
Sepember 9 Projecile moion herefore follows ha of a parabola: 1 a 1 a 1 g 1 g 1 g Equaion of an upside down parabola in and
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