Slide 1Today’s LectureChecklist for TodayAccelerationAccelerationExamplePosition, Velocity and AccelerationImportant Equations of MotionProblem with DerivativesGetting Displacement from VelocityDefinite and Indefinite IntegralsSome IntegralsOur Example with Const. AccelerationHow quickly can you stop a car?Free FallThrow a Ball upProblemSpeederChecklist for TodayPhysics 218Alexei SafonovLecture 4: KinematicsToday’s Lecture•Finish up what’s left from last time•More math issues–Integrals•Problem solving techniques–Motion in 1-Dimension continued–No longer going to use numbers–Examples:•Stopping a speeding car•Free fall •Catching a speederChecklist for Today•For the rest of this week:–Be ready for the lab (WebAssign) including pre-labs and all•Some sections already had labs this week, but not all–Quiz at the recitation on Chapter 1•Same here–There was no pre-lecture for today (this week only, this is not typical)–Homework for Chapter 2 is due Sunday on MP•Coming week recitation quiz will be on Chapter 2–Start Chapter 3 material:•Read the book•Pre-lectures for next week due on SundayAcceleration•Acceleration is the “Rate of change of velocity”•Said differently: “How fast is the Velocity changing?” “What is the change in velocity as a function of time?”dtdVttVVΔtΔVAccel 1212AccelerationExampleYou have an equation of motion of:X = X0 + V0t + ½at2where X0, V0 , and a are constants. What is the velocity and the acceleration? V = dx/dt = 0 + V0 + at•Remember that the derivative of a constant is Zero!! Accel = dV/dt =d2x/dt2 = 0 + 0 + aPosition, Velocity and Acceleration•All three are related–Velocity is the derivative of position with respect to time–Acceleration is the derivative of velocity with respect to time–Acceleration is the second derivative of position with respect to time•Calculus is REALLY important•Derivatives are something we’ll come back to over and over againImportant Equations of MotionIf the acceleration is constantPosition, velocity and Acceleration are vectors. More on this in Chap 3221000tatv x xtav v Problem with Derivatives•A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by –x(t) = bt2 - ct3, b= 2.40 m/s2, c = 0.12 m/s3•Calculate: –instantaneous velocity of the car at t= 0,5,10 s –How long after starting from rest is the car again at rest?Getting Displacement from Velocity•If you are given the velocity vs. time graph you can find the total distance traveled from the area under the curve:–X-X0=V0t + ½at2•Can also find this from integrating…For const acceleration the Equation of motion: X=X0+V0t + ½at2tovdt0x-xDefinite and Indefinite Integralscacbct|cdtca, b, cdtb)d(ctbb ct dt c itiveanti-derivValuebtatba constants) are and (assuming :ends and begins nintegratio of regionmy know where I If equation theof sideright the toadded is andconstant arbitrary an is where)( an is integral an many ways Inintegral? an of thecalculate youHow toSome Integrals mmtmtdtdmdtdat))a((mc) a( dtat)(mm01"derivitive-anti"Check 11111c) a( dt at c at a dt mtmm11 :general more thisMakeOur Example with Const. Acceleration22100221000 )( )( x-x attv|attvdtatvvdtttotoHow quickly can you stop a car?You’re driving along a road at some constant speed, V0, and slam on the breaks and slow down with constant deceleration a. 1. How much time does it take to stop?2. How far do you travel before you come to a stop?When you hit the brakesWhere you stopFree Fall•Free fall is a good example for one dimensional problems•Gravity:–Things accelerate towards earth with a constant acceleration –a=g=9.8m/s2 towards the earth–We’ll come back to Gravity a lot!Throw a Ball upYou throw a ball upward into the air with initial velocity V0. Calculate:a) The time it takes to reach its highest point (the top). b) Distance from your hand to the topc) Time to go from your hand and come back to your handd) Velocity when it reaches your hande) Time from leaving your hand to reach some random height h.Problem•Show that for constant acceleration:202fV-V x)2a( SpeederA speeder passes you (a police officer) sitting by the side of the road and maintains their constant velocity V. You immediately start to move after the speeder from rest with constant acceleration a.•How much time does it take to ram the speeder?•How far do you have to travel to catch the speeder? •What is your final speed?XPolice Officer SpeederChecklist for Today•For the rest of this week:–Be ready for the lab (WebAssign) including pre-labs and all•Some sections already had labs this week, but not all–Quiz at the recitation on Chapter 1•Same here–There was no pre-lecture for today (this week only, this is not typical)–Homework for Chapter 2 is due Sunday on MP•Coming week recitation quiz will be on Chapter 2–Start Chapter 3 material:•Read the book•Pre-lectures for next week due on
View Full Document
Unlocking...