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Representing Motion 
Graphically 
Drawing ggrraapphhss ffoorr kkiinneemmaattiiccss pprroobblleemmss 
SSiiggnniiffiiccaannccee ooff aarreeaa uunnddeerr tthhee ggrraapphh 
SSoollvviinngg pprroobblleemmss tthhaatt rreeqquuiirree aa 
ggrraapphhiiccaall uunnddeerrssttaannddiinngg 
FFrreeeellyy ffaalllliinngg oobbjjeeccttss 
Nelson Pages: 88--1155,, 2200
One of the best types of linear motion problems 
to look at, is a ball being thrown vertically into 
the air. 
 WWee wwiillll aassssuummee tthhaatt tthhee bbaallll rreeaacchheess iittss 
hhiigghheesstt uuppwwaarrdd ssppeeeedd aatt ggrroouunndd lleevveell.. 
 TThhee ssllooppee ooff aa ttaannggeenntt lliinnee ppllaacceedd aannyywwhheerree 
oonn tthhee dd--tt ggrraapphh eeqquuaallss tthhee vveelloocciittyy ooff tthhee 
oobbjjeecctt aatt tthhaatt ttiimmee.. NNoottiiccee tthhaatt tthhiiss ggrraapphh iiss 
ppaarraabboolliicc aanndd tthhee eeqquuaattiioonn ooff mmoottiioonn iiss:: 
ΔdT = v1 ΔΔtt +½ aaΔΔtt22 
 TThhee eeqquuaattiioonn ffoorr vveelloocciittyy,, oonn tthhee vv--tt ggrraapphh,, iiss:: 
vv22 == vv11 ++ aaΔΔtt 
 TThhee aarreeaa uunnddeerr tthhee vv--tt ggrraapphh rreepprreesseennttss tthhee 
ddiissppllaacceemmeenntt.. HHeerree tthhee ttoottaall ddiissppllaacceemmeenntt,, 
ffrroomm ssttaarrtt ttoo eenndd,, eeqquuaallss ____________________.. 
 TThhee ssllooppee ooff tthhee vv--tt ggrraapphh iiss tthhee aacccceelleerraattiioonn 
(wwhhiicchh iiss aa nneeggaattiivvee).. WWee sseeee tthhaatt tthhee ssllooppee 
iiss ccoonnssttaanntt aanndd (lliikkeellyy) eeqquuaallss ______________.. 
 TThhee aarreeaa uunnddeerr tthhee aa--tt ggrraapphh rreepprreesseennttss tthhee 
________________.. 
d 
t 
t 
t 
v 
a 
d v s t 
v v s t 
a v s t
Chalkboard Example 
An object moves with uniform acceleration 
and moves a distance of 200 m [N] in a 
time of 10.0 s. Determine the following:: 
 TThhee vveelloocciittyy ooff tthhee oobbjjeecctt aatt 55..00 ss 
 TThhee vveelloocciittyy ooff tthhee oobbjjeecctt aatt 1100..00 ss iiff iittss 
vveelloocciittyy aatt 33..00ss iiss 1100..00 mm//ss [[NN]].. 
 Ans: 20.0m/s [N] and 45.0 m/s [N].
Practice Questions 
 Workbook ppaaggee 77 QQ##11--44,, PPaaggee 88 ## 33,, 44,, 55,, 
66 –– ccoonnffiirrmm qquueessttiioonnss aanndd aannsswweerrss ffoorr 
ppaaggee 88 
TThheessee QQuueessttiioonnss ccaann bbee uusseedd ffoorr rreevviieeww:: 
 NNeellssoonn PPaaggee 1133 QQ## 22,, PPaaggee 2200 QQ ##11,, 33,, 55

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Grade12-U1-L2-Motion Graphs

  • 1. Representing Motion Graphically Drawing ggrraapphhss ffoorr kkiinneemmaattiiccss pprroobblleemmss SSiiggnniiffiiccaannccee ooff aarreeaa uunnddeerr tthhee ggrraapphh SSoollvviinngg pprroobblleemmss tthhaatt rreeqquuiirree aa ggrraapphhiiccaall uunnddeerrssttaannddiinngg FFrreeeellyy ffaalllliinngg oobbjjeeccttss Nelson Pages: 88--1155,, 2200
  • 2. One of the best types of linear motion problems to look at, is a ball being thrown vertically into the air.  WWee wwiillll aassssuummee tthhaatt tthhee bbaallll rreeaacchheess iittss hhiigghheesstt uuppwwaarrdd ssppeeeedd aatt ggrroouunndd lleevveell..  TThhee ssllooppee ooff aa ttaannggeenntt lliinnee ppllaacceedd aannyywwhheerree oonn tthhee dd--tt ggrraapphh eeqquuaallss tthhee vveelloocciittyy ooff tthhee oobbjjeecctt aatt tthhaatt ttiimmee.. NNoottiiccee tthhaatt tthhiiss ggrraapphh iiss ppaarraabboolliicc aanndd tthhee eeqquuaattiioonn ooff mmoottiioonn iiss:: ΔdT = v1 ΔΔtt +½ aaΔΔtt22  TThhee eeqquuaattiioonn ffoorr vveelloocciittyy,, oonn tthhee vv--tt ggrraapphh,, iiss:: vv22 == vv11 ++ aaΔΔtt  TThhee aarreeaa uunnddeerr tthhee vv--tt ggrraapphh rreepprreesseennttss tthhee ddiissppllaacceemmeenntt.. HHeerree tthhee ttoottaall ddiissppllaacceemmeenntt,, ffrroomm ssttaarrtt ttoo eenndd,, eeqquuaallss ____________________..  TThhee ssllooppee ooff tthhee vv--tt ggrraapphh iiss tthhee aacccceelleerraattiioonn (wwhhiicchh iiss aa nneeggaattiivvee).. WWee sseeee tthhaatt tthhee ssllooppee iiss ccoonnssttaanntt aanndd (lliikkeellyy) eeqquuaallss ______________..  TThhee aarreeaa uunnddeerr tthhee aa--tt ggrraapphh rreepprreesseennttss tthhee ________________.. d t t t v a d v s t v v s t a v s t
  • 3. Chalkboard Example An object moves with uniform acceleration and moves a distance of 200 m [N] in a time of 10.0 s. Determine the following::  TThhee vveelloocciittyy ooff tthhee oobbjjeecctt aatt 55..00 ss  TThhee vveelloocciittyy ooff tthhee oobbjjeecctt aatt 1100..00 ss iiff iittss vveelloocciittyy aatt 33..00ss iiss 1100..00 mm//ss [[NN]]..  Ans: 20.0m/s [N] and 45.0 m/s [N].
  • 4. Practice Questions  Workbook ppaaggee 77 QQ##11--44,, PPaaggee 88 ## 33,, 44,, 55,, 66 –– ccoonnffiirrmm qquueessttiioonnss aanndd aannsswweerrss ffoorr ppaaggee 88 TThheessee QQuueessttiioonnss ccaann bbee uusseedd ffoorr rreevviieeww::  NNeellssoonn PPaaggee 1133 QQ## 22,, PPaaggee 2200 QQ ##11,, 33,, 55