Recilinear Kinemaic Coninuou Moion Sir Iaac Newon Leonard Euler
Oeriew Kinemaic Coninuou Moion Erraic Moion Michael Schumacher. 7-ime Formula 1 World Champion
Kinemaic The objecie of kinemaic i o characerize he following properie of an objec a an inan during i in moion: Poiion Velociy acceleraion Sir Iaac Newon
Kinemaic Aumpion in kinemaic : he objec i negligible ize and hape (paricle) The ma i no conidered in he calculaion Roaion of he objec i negleced We hall look a he kinemaic of an objec moing in a raigh line. We call hi Recilinear Kinemaic
Recilinear Kinemaic: Coninuou Moion Conider a paricle in recilinear moion from a fixed origin O in he S direcion. O S Poiion For a gien inan, i he poiion coordinae of he paricle The magniude of i he diance from he origin (in fee, meer or he relean uni of meaure)
Recilinear Kinemaic: Coninuou Moion Noe ha he poiion coordinae would be negaie if he paricle raeled in he oppoie direcion according o our frame of reference Poiion i ha a magniude (diance from origin) and i baed on a pecific direcion. I i herefore a ecor quaniy
Coninuou Moion - Diplacemen Diplacemen i defined a he change in poiion O S Diplacemen
Coninuou Moion - Diplacemen Diplacemen i alo a ecor quaniy characerized by a magniude and a direcion Noe ha diance on he oher hand i a calar quaniy repreening he lengh from an origin. France Wale. Six Naion Cup. Lineou
Coninuou Moion Aerage Velociy If he paricle undergoe diplacemen oer a ime ineral hen he aerage elociy oer hi ime ineral ag O S Velociy
Coninuou Moion Inan. Velociy If we were o ake maller and maller alue of hen would alo ge maller and maller. A ome poin would no longer be an ineral bu a poin in he ime dimenion (inan). The aociaed elociy i called he inananeou elociy
Coninuou Moion Inan. Velociy By definiion, inananeou elociy lim 0 Alernaely repreened a d d (1) Ye Roy. Rockeman
Coninuou Moion Velociy Velociy i a ecor quaniy If we had moed o he lef, he elociy would be a negaie alue The magniude of he elociy i called peed The uni of elociy (and peed) include f/, mph (mile per hour), m/, kph (kilomeer per hour)
Coninuou Moion Aerage Speed Aerage peed i a poiie calar alue defined a he oal diance diided by he ime elaped p ag T Pi Sop. McClaren Mercede Team, Formula 1
Coninuou Moion Aerage Speed Conider he following moion ha occur oer a ime ineral P P S O Aerage elociy eru aerage peed T T bu p ag ag
Coninuou Moion - Acceleraion If he elociy a wo inance i known hen can obain he aerage acceleraion of he objec during he ime ineral a a ag a O Acceleraion S
Coninuou Moion - Acceleraion If we reduce o an infinieimally mall ineral (aka inan), we ge he inananeou acceleraion a d lim or a () 0 d We can ee ha acceleraion i a ecor quaniy
Coninuou Moion - Acceleraion Commonly ued uni: f/, m/, ec Subiuing Eqn () in Eqn (1); a d d d d d d From Eqn (1) and Eqn () if elociy i conan, hen a = 0 If <, hen we will hae a negaie alue of acceleraion. Thi i called deceleraion
Coninuou Moion - Acceleraion From Eqn (1) we can wrie d d From Eqn () d d a Equaing he aboe a d d (3) Galileo Galilei
Equaion of Moion: Under Conan Conider he following: Acceleraion our acceleraion o be conan, i.e. a = a c a = 0, = 0, and = 0 From Eqn () a c d d Rearranging and inegraing 0 d 0 a c d
Moion Under Conan Acceleraion Soling he definie inegral, we obain elociy a a funcion of ime: 0 ac (4) Subiuing Eqn (4) ino Eqn (1) 0 d 0 d d 0 0 a a c c d
Moion Under Conan Acceleraion we obain poiion a a funcion of ime: 1 0 0 ac We can rearrange Eqn (4) a and ubiue in Eqn (5) 0 a c (5)
Moion Under Conan Acceleraion We obain elociy a a funcion of poiion 0 ac (6) 0 Apollo 11 Launch
Example How Did Tha Go?
Joeph Loui Lagrange Recilinear Kinemaic Erraic Moion
Oeriew Erraic Moion Graphical approach Sample problem Rober H. Goddard (196) Rocke pioneer
Erraic Moion When he moion of an objec i erraic, we canno ue he ingle coninuou funcion o decribe i kinemaic In oher word he acceleraion i no conan Serie of funcion hae o be ued o pecify he moion oer differen ime ineral In general graph are ued o faciliae he calculaion Pierre-Simon Laplace
Velociy = Slope of graph a ime d d 1 d d 1 d d 3 d d 3 Beijing, PRC 0 0 d d 0 1 3 1 O 1 3 O 1 3 3
Acceleraion = Slope of graph a ime d d a a 1 d d 1 a d d a 3 d d 3 3 a Cro Counry Race, MN a 0 d d 0 O 0 1 1 3 a 0 = 0 a 1 a a 3 1 3
Change in elociy from a graph a d a d d a d a d a 0 O 1 a d 1 1 0 O 1
Diplacemen from graph d d d d d 0 O 1 d 1 1 0 O 1
Graph of & a (Velociy) 1 1 1 1 1 a d d a d d a d a 1 1 1 a d O a 0 1 O 1 1 0
Graph of & a (Acceleraion) a d d a d d a d d 0 a 0 d a d O O
Example How Did Tha Go?