Displacement, Velocity And Acceleration

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1 Displacement, Velocity And Acceleation Vectos and Scalas Position Vectos Displacement Speed and Velocity Acceleation Complete Motion Diagams Outline

2 Scala vs. Vecto Scalas vs. vectos Scala : a eal numbe, no diection Examples : mass, chage, enegy, tempeatue, time... Vecto : a scala (its magnitude) and a diection in space Examples : position displacement, velocity, foce, toque, momentum...

3 Vectos have diffeent ules of aithmetic If you add 2 students to a goup of 3 students, how many students do you have? If you walk Noth 3 km and then walk West 4 km, what is you displacement fom whee you stated?

4 Vecto Addition: Vecto + Vecto = Vecto A + B = C A B Tiangle Method Paallelogam Method A B A C = A + B C = A + B B

5 Vecto Multiplication: i) scala vecto = vecto A 3 2 A 1 2 A ii) vecto vecto = scala (dot poduct) F s = W iii) vecto vecto = vecto (coss poduct) p = L

6 Vecto Subtaction: Vecto - Vecto = Vecto A - B = A + (-B) Just like: 3 2 = 3 + (-2)

7 Delta Δ Geek lette fo capital D Physicists use it to epesent change in a quantity Δ Not a symbol which we will use by itself Δ Δ = t 2 1 t Whee thee is a Δ, subtaction is always involved

8 Ex: Vecto Sub Vecto Subtaction Example: 2 1 =? Δ

9 QQ5 Motion Diagam Quick Quiz 6 Which answe best epesents? 2 1 Δ (A) (B) (C) (D)

10 Position Vectos Tells whee something is elative to the oigin of position gaph (usually 2-D o 3-D) The oigin is just a convenient choice of place to measue fom The oigin could be anywhee, but if you choose it caefully, you will likely end up doing less wok A position vecto is ALWAYS measued fom the ORIGIN

11 Position Vectos Ex y What do you need to define a position? oigin x

12 Displacement The point of making position vectos is to make it easie to discuss how things CHANGE thei positions A change in position is called a displacement The displacement vecto is typically witten as Δ A displacement vecto is ALWAYS measued fom the tip of the initial position vecto to the tip of the final position vecto

13 QQ6a Δ y A peson stats at position 1 and ends at position 2, what is thei displacement? x

14 Answe 6a y Δ 2 1 oigin x

15 Answe QQ6c Δ 6c Quick Quiz 7 Δ = 2 1 If, what was 1? A. (10,10) B. (20,0) C. (40, 20) D. (0,0) E. (0,20) y (10,10) (30,10) Δ = (30,10) 2 oigin x

16 Aveage Speed Aveage speed = Distance taveled Time spent taveling OR v avg = Δ Δt Not a vecto! Not a vecto!

17 Example 1 Av Speed Example 1 Aveage Speed If a ca tavels 100 km/h fo an hou, and then tavels 50 km/h fo an hou. The aveage speed is given by: v avg = total distance taveled time spent taveling

18 QQ6 Av Speed Quick Quiz 8 Shaon Donnelly is competing against in a tiathlon. She must fist swim 1.5 km, then bike 40 km, then un 10 km back to the spot whee the ace began. Shaon s aveage speeds ae 0.75 km/h fo swimming, 40 km/h on bicycle, and 10 km/h unning. What is Shaon s aveage speed ove the entie tiathlon? A) 1 km/h B) 9 km/h C) 13 km/h D) 20 km/h E) 32 km/h

19 Aveage Velocity Aveage velocity = Displacement Time spent taveling OR v avg = Δ Δt Vecto! Vecto!

20 QQ7 Av Speed Quick Quiz 9 Shaon Donnelly and Samantha McGlone wee competing against each othe in the tiathlon descibed in Quick Quiz 8. Samantha s aveage speeds ae 0.75 km/h fo swimming, 40 km/h on bicycle, and 10 km/h unning. Who has the highe aveage velocity fo the tiathlon? (A) Shaon has the highe aveage velocity (B) Samantha has the highe aveage velocity (C) They both have the same aveage velocity (D) You need to know the diection of tavel fo the swimming, bicycling and unning potions.

21 Position fom Velocity Δ vavg = Δ = v avg Δt Δt but Δ = = vavg Δ 2 = 1 + ( vavg Δ t t)

22 Acceleation Acceleation is the ate of change of velocity a avg = Δv avg Δt The acceleation vecto ALWAYS points in the same diection as the CHANGE in velocity.

23 Change in Velocity Δv Δv = v v 2 1

24 QQ8a Δv y The ed dots indicate the position of an object at equal time intevals. 1 oigin 2 3 x How do we find the diections and elative magnitudes of the aveage velocity vectos?

25 Answe 8a y v 2 v oigin x How do we find the diections of the aveage acceleation vecto?

26 Answe 8b cont d v 2 v 1 a is in the diection of Δv

27 Answe 8b cont d y a oigin x

28 Pedicting Motion Δ vavg = 2 = 1 + ( vavg Δt) Δt a avg = Δv Δt v v + ( a t) 2 = 1 avg Δ

29 Complete Motion Diagams Dots epesent positions at unifomly spaced time intevals An aow that connects two dots epesents the diection and elative magnitude of the aveage velocity fo the time inteval between those two dots Aows dawn at the dots epesent the aveage acceleation fo the time inteval between the pevious dot and the next dot

30 Complete Motion Diagams

31 QQ10 Motion Diagam A plane flies in a hoizontal cicle without changing speed. Daw the motion diagam fo the plane. What diection does the acceleation vecto point? A) Towad the cente of the cicle B) Away fom the cente of the cicle C) Along the tangent to the cicle D) Thee is no acceleation, since its speed is constant

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