Lecture 4 ( ) Some points of vertical motion: Here we assumed t 0 =0 and the y axis to be vertical.

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1 Sme pins f erical min: Here we assumed and he y axis be erical. ( ) y g g y y y y g dwnwards 9.8 m/s g Lecure 4

2 Accelerain The aerage accelerain is defined by he change f elciy wih ime: a ; In analgy, he insananeus accelerain can be cmpued using he same equain, bu in he limi f ery small elapsed imes. a lim a a ( ) Example: A speed ba sars frm res and reaches 3. m/s in s. Wha is is aerage accelerain? Assuming is accelerain be cnsan, wha is is elciy afer 5 s?

3 Min under cnsan accelerain Recall a. Fr cns. accelerain, a elciy Als: ( ) x and a (, ) ime (,) ( ) Puing i all geher: x x ( ) ( a ) a Fr cnsan accelerain : x a x ( ) a

4 examples A speed ba sars frm res a and x and acceleraes a a rae f a.6 m/s s. Hw far des i g afer 5 secnds? x a.6 m/s 5 s x? Fr cnsan accelerain : x a x ( ) a

5 One mre equain In principle, hese hree equains are enugh. Hweer here is a class f prblems where yu knw,, a, and. One mre equain can make such prblems easier sle. ( ) accelerain : cnsan Fr a x x a ( ) ( ) ( )( ) a x a a a, / / : and wih Replace x a ( ) x a a x x a accelerain : cnsan Fr

6 Example A ruck ming a an iniial elciy f 33 m/s, deceleraes a sp wih a rae f m/s.. Hw far des he ruck rael befre spping? 33 m/s a - m/s x? Fr cnsan a x ( ) x a ax accelerain :

7 Clicker quiz A man is driing his car a a elciy f m/s. Suddenly, he nices ha he car m in frn f him is spped and he slams n his brakes. Because i is winer, he racin is pr and his car deceleraes wih an accelerain f nly 3 m/s. Wih wha elciy des he hi he spped car in frn f him? Selec he answer belw ha is clses he answer ha yu calculae. a) 4 m/s b) m/s c) -4 m/s d) 6.5 m/s m/s a -3 m/s x m?

8 Min diagram under cnsan accelerain A mass a res a is acceleraed wih cnsan accelerain he righ. The min diagram shws he psiin f he mass a, s, s, 3s, 4s, 5 and 6s. The arrws shw he displacemens beween hese psiins. Cnsider x(4) ( ) ( 3) x s and 4 ( ) ( ) x s and 3 ( ) ( 3) a s x ( 3) a s s ( 3) s a ( s) ( ) ( ) a s ( ) ( 3) a s x 3 3 ( 3) a s s ( 3) s a ( s) ( ) x 4 x 3 a ( s) similarly x 5 x 4 a s ec. The displacemens increase by he same amun, a.

9 clicker quesin ) ) 3) 4) These fur min diagrams shw he min f a paricle alng he x-axis, where he psiie direcin is he righ. Sme f hem depic psiie accelerains, and sme depic negaie accelerains. Which are which? a) & are psiie, 3&4 are negaie b) &3 are psiie, &4 are negaie c) &4 are psiie, &3 are negaie d) &3 are psiie, &4 are negaie Hins: Ging in he ppsiie direcin means he sign is changed. Als 3)has psiie accelerain.

10 (m/s) Graphical deerminain f displacemen (m/s),, (s) (s) )Wha is he displacemen cered in secnd? )Wha is he area indicaed by? Hin: Use x /a r x.5*( ) The area under he - cure is equal he displacemen f he bjec! Ne uni f area: aream/s*sm Q.. x (m) area(m) a).. b).. c).. d).. Laer, we will use fac ha he area under he a- cure is equal he elciy f he bjec! Ne uni f area: aream/s *sm/s in ha case

11 Example Imagine a car ming saring a res a x and haing he fllwing accelerain as a funcin f ime. Wha is he elciy and psiin a s and a 4 s? Fr cnsan a: a; x x a ; x x ( ) Can use area ge () and (4) ()a(m/s )(s)m/s (4)() am/s(m/s )(s) (4)6 m/s x by mre bius rue xx /a x()(s)/(m/s )(s) m x(4)mm/s(s)/(m/s )(s) x(4)m4m4mm x by less bius rue use x()x.5*( ) ge x() x().5*(m/s)(s)m x(4)m.5*(m/s6m/s)(s)m

12 Cncepual Reading Quiz If yu drp an bjec in he absence f air resisance, i acceleraes dwnward a 9.8 m/s. If insead yu hrw i dwnward, is dwnward accelerain afer release is: a) less han 9.8 m/s. b) 9.8 m/s. c) mre han 9.8 m/s. I ain' wha yu dn' knw ha ges yu in ruble. I's wha yu knw fr sure ha jus ain' s. Mark Twain

13 Min under Earh s graiainal aracin Near he Earh s surface, all bjecs are acceleraed by graiy dwnwards wih an accelerain f g9.8 m/s. g 9.8 m/s dwnwards g y y y y g gy ( ) A imed drp can pride ne measuremen f g. hp://

14 Example A Lucy hrws a ball sraigh upwards wih a elciy f 3 m/s. I rises a disance h and hen falls dwnward where Lucy caches i. ) When des he ball sp? ) Hw high des i g? g 9.8 m/s g y y y y g gy dwnwards ( ) 3 m/s? h?

15 Example A Lucy hrws a ball sraigh upwards wih a elciy f 3 m/s. I rises a disance h and hen falls dwnward where Lucy caches i. ) When des he ball reurn Lucy s hand? ) Wha is is elciy when Lucy caches i? a) 3 m/s b) 6 m/s c) 3 m/s d) 6 m/s g 9.8 m/s g y y y y g gy dwnwards ( ) 3 m/s y??

i-clicker Question lim Physics 123 Lecture 2 1 Dimensional Motion x 1 x 2 v is not constant in time v = v(t) acceleration lim Review:

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