Linear Motion. Kinematics Quantities

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1 Liner Motion Physics 101 Eyres Kinemtics Quntities Time Instnt t Fundmentl Time Interl Defined Position x Fundmentl Displcement Defined Aerge Velocity g Defined Aerge Accelertion g Defined 1

2 Kinemtics Quntities Sclers: Mgnitude Time Instnt, Time Interl nd Speed Vectors: Mgnitude nd Direction Position, Displcement, Velocity, Accelertion Don t Forget Units! Coordinte System Estblish the coordinte system ruler A number line with rrow showing positie direction. Any direction you choose. The x=0 (or y=0) loction is identified. Agin it cn be ny plce your choose. x=0

3 Position Estblish the coordinte system ruler Red the position from the ruler Don t forget the units nd direction. Positie Positions x=0 Negtie Positions Velocity Estblish the coordinte system ruler Velocity direction is positie in direction of coordinte system. Velocity direction cn lso be clculted from displcement becuse = Positie Positions x=0 Negtie Positions 3

4 Motion Digrms Specilized Digrm tht includes most of the kinemtics informtion. Used s tool to sole kinemtics problems. Motion Digrm templtes re ilble to print from the clss website. Motion Type I Constnt or Speed up or Slow Motion Type II Constnt or Speed up or Slow Motion Type III Constnt or Speed up or Slow = t = = t = = t = = t = Prt I: Equtions Prt II: Equtions Prt III: Equtions Circle the known lues Circle the known lues Circle the known lues 4

5 Problem Soling Process Problem Description: This is generlly gien. You must identify in the text gien, the question tht must be nswered. Physics Description: Digrms nd equtions relent to the sitution. Solution: The lgebr, grphs, etc. And the nswer to the question! Eluttion: Check your units, mgnitude, direction nd mtching between representtions.. Problem Description Exmple A person is treling left t 10 m/s for min. How fr does this person trel? 5

6 Physics Description =10 m/s t =10 sec Constnt 0 0 =10 m/s t =0 A person is treling left t 10 m/s for min. How fr does this person trel? = Solution =10 m/s t =10 sec Constnt 0 = 0 =10 m/s t =0 A person is treling left t 10 m/s for min. How fr does this person trel? m s m s = 10s ( 10s) = = 100 m 6

7 Elute A person is treling left t 10 m/s for min. How fr does this person trel? Unit Anlysis m s = m s Mgnitude 100 m is bout 3/4 mi Must be riding in ehicle Definition of g. elocity Both sides of eqution re equl Mgnitude Units Direction (it is ector!) Velocity = Mgnitude = Mgnitude Units = Units Direction = Direction 7

8 Rte of Chnge of Rte of Chnge of Position Slope is Rise/Run = 8

9 Problem Description Find the direction (+/-) of the elocity in the time interls () 0 to 3 s (b) 4sto5s s (c) 0 to 5 s (d) to 4 s (e) 3 to 4 s Exmple All these Velocities? Chnge in Velocity: Δ = lter elocity minus erlier elocity lter erlier Aerge Velocity: = Between ny times If elocity increses regulrly then find erge of i nd f. Slope of stright line between points Instntneous Velocity Between times just bit fter/before t Slope of tngent line t t = ( + ) i f 9

10 Exmple Problem Description Find the erge elocity in the time interls () 0 to 1s (b) 0 to 3 s (c) 4sto5s s (d) 0 to 5 s (e) to 4 s (f) 3 to 4 s Exmple Problem Description Find the instntneous elocity t the time () s (b) 3 s (c) 05s

11 Finding the Aerge Chnging Velocity 1, 4, 7, 8, 9, 15, 35 1, 4, 7, 10, 13, 16, 19 4, 8, 1, 16, 0, 4, 8 Requlrly chnging elocity: Aerge the 1 st nd Lst + = The middle lue Velocity increses from 10 to 0 m/s: g. =? i f Cn you Identify Instntneous nd Aerge Velocities? Fster nd Slower Speeds? 11

12 Definition of ccelertion Both sides of eqution re equl Mgnitude Units Direction (it is ector!) Accelertion = Δ Mgnitude = Mgnitude Units = Units Direction = Direction Signs cn get us Direction Depend on Coordinte System Choice =+10 =+ Δ = (+) - (+10) Δ = -8 x=0 So ccel is negtie! 1

13 Accelertion Estblish the coordinte system ruler Drw elocity rrows. Accelertion direction cn be clculted from elocity becuse Δ x=0 Mke up smple numbers: 1 = - 5m/s = -8 m/s V-1 =[ -8 (-5)] m/s Δ = -3 m/s so is negtie Accel. Is negtie Reiew of Equtions Fundmentl Definition of Aerge Velocity. This is not Δ! = Δ x Fundmentl Definition iti of Aerge Accelertion. = Δ 13

14 Eqution Nottion Simplify by setting t 1 =0 Think of it s =t Other simplified nottion nd ssumptions = f = g nd is Constnt Δ Δ t Δ t t = Δ t = t = 0 f 0 + t = i Reiew of Equtions A combintion of other equtions My be used only if: Accelertion is constnt Initil t is zero or t mens = i t + 1 t 14

15 Equtions: from your text A combintion or rerrnged My be used only if: Accelertion is constnt Initil t is zero or t mens Rte of Chnge of Rte of Chnge of Velocity Slope is Rise/Run Δ 15

16 Coordinte Red from Grph On n x s t grph the coordinte tells us the position (x) nd the time instnt (t). Slope On n x s t grph the slope tells us the elocity. Are UNITS Gie us the CLUES! Coordinte Red from Grph On n s t grph the coordinte tells us the nd the Slope On s t grph the slope tells us the. Are UNITS Gie us the CLUES! 16

17 Coordinte Red from Grph On n s t grph the coordinte tells us the elocity nd the time instnt Slope On s t grph the slope tells us the ccelertion. Are UNITS Gie us the CLUES! Signs? Depend on Coordinte System Choice x=0 Wht is the sign of: xi, xf,, i, f, Δ,? 17

18 Signs? Depend on Coordinte System Choice x=0 Wht is the sign of: xi, xf,, i, f, Δ,? 0, +, +, +, +, -, - Signs? Depend on Coordinte System Choice x=0 Wht is the sign of: xi, xf,, i, f, Δ,? 18

19 Signs? Depend on Coordinte System Choice x=0 Wht is the sign of: xi, xf,, i, f, Δ,? -, +, +, +, +, -, - Signs? Depend on Coordinte System Choice x=0 Wht is the sign of: xi, xf,, i, f, Δ,? 19

20 Signs? Depend on Coordinte System Choice x=0 Wht is the sign of: xi, xf,, i, f, Δ,? +, -, -, -, -, +, + Now cn you plot this? Depend on Coordinte System Choice x s. t s. t?? x=0 0

21 Now cn you plot this? Depend on Coordinte System Choice x s. t s. t x=0 Exmple: 1 prt problem Problem Description A person is treling left beginning t 10 m/s nd slowing down for min. before stopping. How fr does this person trel? 1

22 Physics Description = 0 m/s t =10 sec Slowing 0 =10 m/s t =0 Note: Velocities re positie. Accelertion is neg. since Δ is neg. = = Δ = i t + 1 t = 0 m/s t =10 sec = Slowing Solution 0 =10 m/s t =0 Δ = = t 1 i + t Use circled eqution Find erge elocity first m m 10 s + 0 s = m = 5 s Now cn find displcement = Δ t m 5 s = (10s 0s) = 600m

23 Elute A person is treling left beginning t 10 m/s nd slowing down for min. before stopping. How fr does this person trel? Unit Anlysis m s = m s Mgnitude 600 m is less thn when speed ws constnt. Exmple : Multi-Prt Prob Problem Description A truck on stright rod strts from rest nd ccelertes t.0 m/s until it reches speed of 0 m/s. Then the truck trels for 0 s t constnt speed until the brkes re pplied, stopping the truck in uniform mnner in n dditionl 5.0 s. Wht is the erge elocity of the truck during the motion described? 3

24 Physics Description Prt 1: Motion Type? = t = = t = Coordinte System? Strobe Photo? Velocity ectors? Accel. Vector? = Δ = t 1 i + t Physics Description Speed Up Prt 1: Motion Type? 0 =0 m/s t =0 sec m/s =0 m/s t = Coordinte System? Strobe Photo? Velocity ectors? Accel. Vector? = Δ = t 1 i + t 4

25 Physics Description: Prt Speed Up 0 =0 m/s t =0 sec m/s = =0 m/s t t = = t = Δ x = Δ = Δ = t 1 i + t = t 1 i + t Physics Description: Prt Speed Up Constnt 0 =0 m/s t =0 sec m/s = =0 m/s t t = 0 = 0 m/s t = (nother 0) Δ x = Δ = Δ = t 1 i + t = t 1 i + t 5

26 Physics Description: Prt 3 Speed Up Constnt Slow Down 0 =0 m/s t =0 sec m/s = =0 m/s t t = 0 = 0 m/s t = (nother 0) = 0 t = (nother 5) Δ x = Δ = Δ = Δ = t 1 i + t = t 1 i + t = t 1 i + t Solution Circle things known in equtions Sole for wht you cn Keep going until eerything is known 6

27 Solution Speed Up Constnt Slow Down 0 =0 m/s t =0 sec m/s =100 m = =0 m/s t t = 10 s m = 0 m/s t = 30 s -4 m/s 550 m = 0 t = 35 s Δ x = Δ = Δ = Δ = t 1 i + t = t 1 i + t = t 1 i + t Elute Unit Anlysis? Mgnitudes Resonble? Do the Signs mtch the Arrows? 7

28 Exmple 3: Free Fll Problem Description An pple flls from tree from distnce of.0 m boe the top of the grss below. While flling, it hs downwrd ccelertion of 9.8 m/s. As the pple sinks into the grss, its speed decreses until it stops fter sinking m into the grss. Sole for eerything. Motion Type I Constnt or Speed up or Slow Motion Type II Constnt or Speed up or Slow y = = t = y = = t = Prt I: Equtions Circle the known lues = = i t + Δ 1 t Prt II: Equtions Circle the known lues Δ = = i t + 1 t Motion Type III Constnt or Speed up or Slow y = = t = Prt III: Equtions Circle the known lues = = i t + Δ 1 t = t = 8

29 Solution Circle things known in equtions Sole for wht you cn Keep going until eerything is known Motion Type I Speed up y =.0 m = 0 t = m/s Prt I: Equtions Circle the known lues = = i t + Δ 1 t Motion Type II Slow y = 0 = -6.6 m/s t = 0.64 s +391 m/s Prt II: Equtions Circle the known lues Δ = = i t + 1 t y =-0.05 m = 0 t = 0.66 s 9

30 With Different y=0 Motion Type I Speed up y =.05 m = 0 t = m/s Prt I: Equtions Circle the known lues = = i t + Δ 1 t Motion Type II Slow y = 0.05 m = -6.6 m/s t = 0.64 s +391 m/s Prt II: Equtions Circle the known lues = = i t + Δ 1 t y = 0 m = 0 t = 0.66 s Elute Unit Anlysis? Mgnitudes Resonble? Do the Signs mtch the Arrows? 30

x=0 x=0 Positive Negative Positions Positions x=0 Positive Negative Positions Positions

x=0 x=0 Positive Negative Positions Positions x=0 Positive Negative Positions Positions Knemtc Quntte Lner Moton Phyc 101 Eyre Tme Intnt t Fundmentl Tme Interl Defned Poton x Fundmentl Dplcement Defned Aerge Velocty g Defned Aerge Accelerton g Defned Knemtc Quntte Scler: Mgntude Tme Intnt,