Answers to Homework. After studying the acceleration and velocity graphs you made, answer the following questions.

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Oswald Thornton
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1 Answrs Hmwrk HOMEWORK: NTRODUCTON TO MOTON--CHANGNG MOTON Afr sudyng h alran and vly graphs yu mad, answr h fllwng qusns. +1 A ~------~ (! \., ~ " s.. "" 10 Tm ~ 1. An bj mvng alng a ln (h + dsan axs) has h alran-m graph abv. Hw mgh h bj mv ra hs graph A. f s mvng away frm h rgn s sdn up a a sadv ra (nsanly nrasng vly). B. f s mvng ward h rgn s slwng dwn a a sady ra (nsanly drasng vly). 2. Skh n h axs blw h vly-m graphs ha g wh h abv alranm graph (fr ass A and B). Labl yur graphs. 0 Y (s ) Tls fr Snf Thnkng Hmwrk fr "Changng Mn" ll-s Mn and Fr 9/ CSMT Tufs U. )04

2 B 3. Hw wuld an bj mv ra ah f h hr labld pars f h alran-m graph abv? A:Away frm h rgn, spdng UP a a sady ra, r ward h rgn Slwng dwn a a sady ra. B:A rs r wh a say (nsan) vly. C:Away frm h rgn slwng dwn a a sadv ra r ward h rgn, spdng up a a say ra. 4. Skh blw a vly-m graph whh mgh g wh h abv alran-m graph..' v 1! d~"""""""'"''''''''''''''''''''''''''''''''''';''''''''''''''''''''''m''''''''' M.... C lo ! ~ f! - :.... T m (s ) 10 Ths ar w pssbls. 5. Fr ah f h vly-m graphs blw, skh h shap f h alran-m graph ha gs wh. (Answrs ar xampls f many pssbls.) Y ~ +! +: - ~h "'''''~''''2'''''''''' ''''' '''l M'''''M'''''''''''8'''''' ''M'' '''''rat j m (s )!..~ ~! ~ ~ ~ ~------~ j r a : n _; O~""'"'''''''''''''Y'''''M''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' Tm (s ) Tls fr Snf Thnkng Tahrs' Currulum Gud T-16 Mn and Fr 9/ CSMT Tufs u. (05

3 C Y ~ +1 C f : ~ ~. f Tm (s C) ~.,~j...;..-.l ll>... 0 ~ / ~ - n Tm (s ) Y ~.. ::::.. ~..--=:! Tm (s ) ~ A + '.= C : C f! " " Tm (5 C) ~, n :. 6. A ar mvs alng a ln [h + dsan (psn) axs]. Fll n h abl blw wh h sgn (+ r -) f h vly and alran f h ar fr ah f h mns dsrbd.. Dsan ralraln [\lrtn (Psn) ly Spdng Slwng U Dwn Car mvs away frm h rgn Car mvs ward h rgn Tls fr Snf Thnkng Tahrs' Currulum Gud m-r Mn and Fr 9/ CSMT Tufs U.

4 7. Whh psn-m graph blw uld b ha fr a ar ha s sadly alrang away frm h rgn? C a) b) ) D D D 1 s s S Tm Tm Tm 8. Dsrb hw yu wuld mv prdu h vly m graph n h rgh. Mv away frm h rgn, slwng dwn a a sady ra. Rvrs drn and spd up ward h rgn up a a sady ra. 9. Skh a dsan-m graph graph fr hs mn n h axs n h rgh. v ; ; 1!.. :.. : ~- - - : fm! r Y - D : + S! a n : ~ ; : "..";"... : : \.Tm 10. Skh an alran-m graph fr hs mn n h axs n h rgh. A 1 ~ ~ ~.~.. ~ : : _ -:._ \! '. ~ Tm Tls fr SdnfThnkng Tahrs' Currulum Gud -18 Mn and Fr 9/ CSMT Tufs U. 101

5 A ar an mv n hr drn alng a ln (h + dsan axs). Skh vly-m and alran-m graphs whh rrspnd ah f h fllwng dsrpns f h ar's mn. 11. Th ar sars frm rs, and mvs away frm h rgn nrasng s spd a a sady ra. ~ +1 0' - : y. : ~~ Tm A+l ~----~------~ O~..u -l... ; u l :. :. ~. :. Tm 12. Th ar s mvng ward h rgn a a nsan vly. +!. O... :.' : \ u -... :.. Tm! - : y A+l C O; ~ : 1 Tm -, 13. Th ar sars frm rs, and mvs ward h rgn, spdng up a a sady ra. +: n -; y E l.., Tm y, Al :." C OL...~. ~ " " ".\. 1 : : Tm l~ ~ ~ ~ _ - : Tls fr Snf Thnkng Tahrs' Currulum Gud -19 Mn and Fr 9/ CSMT Tufs U.

6 14. Th fllwng s a vly-m graph fr a ar. + 4! v L 1 ~ : Of...., , /,... Tm (s ) jo y mls! - 4! Wha s h avrag alran f h ar? Shw yur wrk blw. a=l1vll1= (4-1)/(10-0) = 0.30 m/s2 _ 15. A ball s ssd n h ar. mvs upward, rahs s hghs pn and falls bak dwnward. Skh a vly-m and an alran-m graph fr h ball frm h mmn lavs h hrwr's hand unl h mmn jus bfr rahs hr hand agan. Cnsdr h psv drn b upward. +5! ;!,, _ ,. ~!: - : +1 ~ C O~ ~ J. -r-.j : Tm _ -1 Tls fr Snf Thnkng Tahrs' Currulum Gud l-20 Mn and Fr 9/ CSMT Tufs U.

7 Th graphs n hs pag rprsn h mn f bjs alng a ln whh s h psv dsan ( ) (psn) axs. N ha h mn f bjs s rprsnd by dsan, vly, r alran graphs. Answr h fllwng qusns. Yu may us a graph mr han n r n a all, and hr may b mr rr hs han blanks. f nn f h graphs s rr, answr J. ~16. Pk n graph ha gvs nugh nfrman nda ha h vly s always ngav. r +,. Tm D s + v + ~ ; Tm Pk hr graphs ha rprsn h mn f an bj whs vly s nsan (n hangng). ~17. -L (Th answrs an b n any rdr.) ~20. Pk n graph ha dfnly ndas _'_21. an bj has rvrsd Pk n graph ha mgh pssbly b ha f an bj sandng sll Pk 3 graphs ha rprsn h mn f bjs whs alran s hangng. ~22. -L23. ~24. (Th answrs an b n any rdr.) Pk a vly graph and an alran graph ha uld dsrb h mn f h sam bj durng h m shwn. C 25. ly graph. ---.J:L26. Alran graph. r E 1 ~~~... Tm -; <D+~ O: l Tm -: +1 ~ j. ~ -: Tm A +! ~l~... _! Tm A +j 01. C j Tm -, (!) A + 0 lm Tls fr Snf Thnkng Tahrs'.Currulurn Gud -21 Mn and Fr 9/ CSMT Tufs U. 11 0

8 A pnny s ssd n h ar. mvs upward, rahs s hghs pn and falls bak dwnward. Cnsdr h psv drn b upward.. Fr ah f h hr pars f h pnny's mn, us n f h fllwng hs nda whhr h alran s A. + B. - C. 0 Th pnny s mvng upward. Th pnny s a s hghs pn. Th pnny s mvng dwnward. ~ D., r A y ar s gvn a push up an nlnd ramp. rlls up. rahs s hghs pn and rlls bak dwn agan. Cnsdr h psv drn b dwn h ramp. Psv Dm:n~ Fr ah f h hr pars f h ar's mn, us n f h fllwng hs nda whhr h alran s A. + B. - C. 0 ~.3. Th ar s mvng up h ramp. L31. Th ar s a s hghs pn. ~3;( Th ar s mvng dwn h ramp. Whh psn-m graph blw uld b ha fr a ar ha s sadly alrang away frm h mn rgn? a) b) ) D D D s $ s - l l C 33. T m T m. Tm Tls fr Sanf Thnkng - FPSE nrdudol Mn-Changng Mn H-9 MnH~ (shr) 8115/88 C1988CSMJTus U. \ )

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