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# Week Two 221

TCTC

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This 7 page Class Notes was uploaded by Bailey Knapp on Monday August 31, 2015. The Class Notes belongs to 221 at Tri-County Technical College taught by Donny W. Winkler in Summer 2015. Since its upload, it has received 61 views. For similar materials see University Physics I in Physics 2 at Tri-County Technical College.

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I was sick all last week and these notes were exactly what I needed to get caught up. Cheers!

-*Patricia Kling*

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Date Created: 08/31/15

Physics 221 Week Two Graphing Say you gather some data for position and time and put it in a data table And when that data is graphed with a line best fit it looks like this A Xm ts A linear position vs time graph means the velocity is constant Positive means the object is moving the right In physics graphs have a physical meaning Say you gather some data for position and time and put it in a data table l t f When the data is graphed and the points connected it looks like this A lel Ax v lim At gt0 At dx dt Find the slope of the tangent line to find the instantaneous velocity 17 ts A nonlinear position vs tim e graph means the velocity is changing Changing position and speed Example xt 2t2 x t vt vt 4t vtZs 4ms 25 vZs 80 ms A y lvms x 3 f tth vt 2 4t The area x x0 4t dt below the curve xt th xt ts 7 Turning Point 9 Point where velocity is instantaneously equal to zero and then the object reverses direction 9 An example ofthis is when you throw a ball up in the air and it reaches the highest point it is a rest for an instant then immediately turns and falls back towards the ground 1 A vms A 2 M 10 1 A 52sx1oms 5 A 10m A xt gt ts 5 1 3 4 Turning point 10 at t 25 If x0 30m what s the position of the turning point x x0 vtdt 30m 10m 40m Example T6 Dturning point ilo 20 30 4o 50 39 1215 10mS 5 77132 t x x0 fvtdt x 2 30m f10mS 5 mSztdt 5m x 2 30m 10mS t 2 5262 0 30m 10t ms 52t2 mSZ lt1o msgt i J 10 maz 4 75 am t 5 27 ti ZSOI t6S Acceleration 9 Change in velocity over time 9 Describes the rate that velocity changes as a function of time the concept of motion is relative to something else and is not absolute Av 122 v1 At t2 t1 9 UhltSImSZ 9 Can be positive or negative Cl f positive the velocity and acceleration vectors are in the same direction f negative the velocity and acceleration vectors are in different directions 9 Vector quantity 9 Average acceleration Av 61 At 9 Instantaneous acceleration dv dzx a 11m a At gt0 At dt dt2 A vms AV Slope a At ts Motion with Constant Acceleration X1Xo V1Vo t10 X2X1 V2V1 t2t AV Vz Vl V VO a At tz tl t VV0at Kinematic Equations V V0 at V0 V V 2 Valid if and only if 1 2 acceleration is constant X X0 V0t at V2 2 V02 2ax x0 Example A ship is cruising at a speed of 63 ms at the instant it passes by a buoy At this time it begins to increase speed with a constant acceleration of 020 msz How far is the ship from the buoy when its speed is 86 ms V2 2 V02 2ax x0 86 ms2 2 63 ms2 2O20 mSZX0 86 ms2 2 63 ms2 O4O mszx 7396 ms 2 3969 ms 040x ms2 3427 ms 2 040x ms2 85675 m x 85m Free Fall An object falls freely through Earth s atmosphere under the influence of gravity Interest in free fall started with Galileo he rolled objects down inclines of increasing angles until it was vertical All objects fall at the same rate regardless of their mass in the absence of air resistance Air resistance doesn t change the physics it s just an added complication it depends on the object s size density and speed lxl lxl 9 Free fall acceleration is 980 ms2 g 32 ftsz 9 Vector quantity directed towards the center of Earth 9 Acceleration due to gravity not gravity s acceleration Kinematic Equations for Free Fall VV0gt V0V V 2 1 2 V2 2 V02 280 Y0 Example A flower pot falls from a 2ncl story window below V2 2 V02 280 Y0 V2 Zgy V m v J2 980 30m v 5882 S v77 S OR What is its speed just before it hits the ground 30m yyvotgt2 l 2 Y 2 8395 t2 Q g t 3 g t 230m 980532 t 0785 For kinematic problems there is often more than one way to go about solving the problem use the equation that you re most comfortable with Graphical Analysis 9 Plots of position velocity and acceleration and how they are related 1 Constant Position AX Vl 2 Constant Velocity AX Slope v gtt 3 Constant Acceleration LL 7 t V LL 1 rr V V tI Vl The position velocity and acceleration graphs of the same particle s path X A gtlt gtm v V cl

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