Chapter 2. Motion along a straight line

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1 Chaper Moion along a sraigh line Kinemaics & Dynamics Kinemaics: Descripion of Moion wihou regard o is cause. Dynamics: Sudy of principles ha relae moion o is cause. Basic physical ariables in kinemaics and dynamics: Time Posiion Displacemen Velociy Acceleraion

2 Par Time, Posiion, Velociy, Acceleraion 3 Time Time: ha par of eisence which is measured in seconds, minues, hours, days, weeks, monhs, years, ec., or his process considered as a whole Cambridge Dicionary Time: somehing ha is measured in minues, hours, years ec using clocks Clocks: an insrumen in a room or in a public building ha shows wha ime i is Longman Dicionary of Conemporary English 4

3 Time Time is like a rier flowing. Newon Zei is wass enie Uhr mass. Einsein ( Time is wha a clock measures. ) Time is space beween eens Feynman "Time is ha qualiy of naure which keeps eens from happening all a once Anonymous Time is neiher young nor old a beginning or an end, now or foreer; ime is he empy disance in beween. 5 Posiion and Displacemen 6 3

4 Trajecory 7 Velociy 8 4

5 Velociy and Speed 9 Insananeous elociy 5

6 Acceleraion Analyic represenaion 6

7 Velociy and acceleraion 3 One-Dimensional (-D) Moion 4 7

8 Par Moion wih consan Acceleraion 5 Consan Acceleraion 6 8

9 Calculaing posiion 7 Summary able of resuls 8 9

10 D moion wih consan acceleraion a a a he sysem of equaions wih si ariables ma: wo unknowns case : we may eliminae ime from he sysem a( ) case : we may eliminae acceleraion from he sysem ( ) 9 eample a a

11 eample a a eample a a a( )

12 problem. a a The caapul of he aircraf carrier USS Abraham Lincoln acceleraes an F/A-8 Horne je figher from res o a akeoff speed of 73 mph in a disance of 37 f. Assume consan acceleraion.. Calculae he acceleraion of he figher in m/s.. Calculae he ime required for he figher o accelerae o akeoff speed. Gien:. m / s. m 37 f m 73. mph m / s calculaions a( ) a 3. m / s ( ) 3 problem.36 a a A he insan he raffic ligh urns green, a car ha has been waiing a an inersecion sars ahead wih a consan acceleraion of 3. m/s. A he same insan a ruck, raeling wih a consan speed of. m/s, oerakes and passes he car. How far beyond is saring poin does he car oerake he ruck? Gien:. m. m/s c. m/s c a. m/s a c 3. m/s c a a c c a( ) objecs 4 equaions ime is he same.5a c 4

13 Par 3 Free Fall 5 Free fall y g y g 6 3

14 eample y g y g.m / s y 3. m 7 Soluion (con) y g y g.m / s y 3. m 8 a( ) 4

15 The second quesion y g y g.m / s y 3. m 9 Soluion for he second quesion 3 5

16 Discussion of resul for quesion 3 The hird quesion 3 6

17 Being pracical: D moion wih cons. a. iniial alue problem: knowing iniial condiions (, ) and acceleraion a, one may find (,) a any momen in ime.. who cares abou ime hen he sysem of equaion can be reduced o a simple equaion 3. wo objec problem in his case we need co consider a sysem of 4 equaion wih he same ime ariables. In mos problems we need only a couple equaions from he sysem a a a( ) a a a a 33 eample The engineer of a passenger rain raeling a 5. m/s sighs a freigh rain whose caboose is m ahead on he same rack. The freigh rain is raeling a 5. m/s in he same direcion as he passenger rain. The engineer of he passenger rain immediaely applies he brakes, causing a consan acceleraion of -. m/s, while he freigh rain coninues wih consan speed..will he cows nearby winess a collision?. If so, where will i ake place?. m 5. m / s a. m / s a. m 5. m / s. m / s 34 7

18 8 35 a a a a /. / 5.. s m a s m m /. / 5.. s m a s m m a a. a collision means soluions:.5 s 77. s negaie soluions?

4.5 Constant Acceleration

4.5 Constant Acceleration 4.5 Consan Acceleraion v() v() = v 0 + a a() a a() = a v 0 Area = a (a) (b) Figure 4.8 Consan acceleraion: (a) velociy, (b) acceleraion When he x -componen of he velociy is a linear funcion (Figure 4.8(a)),