Page 1Physics 207 – Lecture 3Physics 207: Lecture 3, Pg 1Physics 207, Physics 207, Lecture 3, Sept. 10Lecture 3, Sept. 10Assignment: Assignment: 1.1.For Monday: Read Chapter 4For Monday: Read Chapter 42.2.Homework Set 2 Homework Set 2 (due Wednesday 9/17)(due Wednesday 9/17)Goals (finish Chap. 2 & 3) Goals (finish Chap. 2 & 3) Understand the relationships between position, Understand the relationships between position, velocity & acceleration in systems with 1velocity & acceleration in systems with 1--dimensional dimensional motion and nonmotion and non--zero acceleration (usually constant)zero acceleration (usually constant)Solve problems with zero and constant acceleration Solve problems with zero and constant acceleration (including free(including free--fall and motion on an incline)fall and motion on an incline)Use Cartesian and polar coordinate systemsUse Cartesian and polar coordinate systemsPerform vector algebraPerform vector algebraPhysics 207: Lecture 3, Pg 2Position, velocity & acceleration for motion Position, velocity & acceleration for motion along a linealong a line If the position x is known as a function of time, then we can find both the instantaneous velocity vxand instantaneous acceleration axas a function of time!vxtxtaxt22vadtxddtdxx==dtdxx=v] offunction a is [ )(txtxx∆∆=Page 2Physics 207 – Lecture 3Physics 207: Lecture 3, Pg 3Position, displacement, velocity & accelerationPosition, displacement, velocity & acceleration All are vectors and so vector algebra is a must ! These cannot be used interchangeably (different units!)(e.g., position vectors cannot be added directly to velocity vectors) But we can determined directions “Change in the position” vector gives the direction of the velocity vector “Change in the velocity” vector gives the direction of the acceleration vector Given x(t) vx(t) ax(t) Given ax(t) vx(t) x(t)vrarPhysics 207: Lecture 3, Pg 4And given a And given a constant accelerationconstant accelerationwe we can integrate to get explicit can integrate to get explicit vvxxand and aaxxxaxvxttttxxx∆+= avv02210 a v0ttxxxx∆+∆+=consta=x22vadtxddtdxx==dtdxx=v] offunction a is [ )(txtxx∆∆=0x0Page 3Physics 207 – Lecture 3Physics 207: Lecture 3, Pg 5 A “biology” experiment Hypothesis: Older people have slower reaction times Distance accentuates the impact of time differences Equipment: Ruler and four volunteers Older student Younger student Record keeper Statistician Expt. require multiple trials to reduce statistical errors.20 )( Exploiting txx∆∝−Physics 207: Lecture 3, Pg 6Rearranging terms gives two other relationshipsRearranging terms gives two other relationships For constant acceleration: From which we can show (caveat: a constant acceleration))v(v21v)x(x2av vxx(avg)x 0x2x2x00+=−=−txxx∆+= avv02210 a v0ttxxxx∆+∆+=consta=xaxtPage 4Physics 207 – Lecture 3Physics 207: Lecture 3, Pg 7AccelerationAcceleration Changes in a particle’s motion often involve acceleration The magnitude of the velocity vector may change The direction of the velocity vector may change (true even if the magnitude remains constant) Both may change simultaneouslyvv11vv00vv33vv55vv22vv44aaaaaaaaaaaavatt0v(t)=v0+ a ∆ta ∆t = area under curve = ∆v∆tPhysics 207: Lecture 3, Pg 8Acceleration has its limitsAcceleration has its limits“High speed motion picture camera frame: John Stapp is caught in the teeth of a massive deceleration. One might have expected that a test pilot or an astronaut candidate would be riding the sled; instead there was Stapp, a mild mannered physician and diligent physicist with a notable sense of humor. Source: US Air Force photoPage 5Physics 207 – Lecture 3Physics 207: Lecture 3, Pg 9Free FallFree Fall When any object is let go it falls toward the ground !! The force that causes the objects to fall is called gravity. This acceleration on the Earth’s surface, caused by gravity, is typically written as “little” g Any object, be it a baseball or an elephant, experiences the same acceleration (g) when it is dropped, thrown, spit, or hurled, i.e. g is a constant. Physics 207: Lecture 3, Pg 10When throwing a ball straight up, which of the When throwing a ball straight up, which of the following is true about its velocity following is true about its velocity vvand its and its acceleration acceleration aaat the highest point in its path?at the highest point in its path?A.A.BothBothv = 0v = 0andanda = 0a = 0B.B.v v ≠≠00, but , but a = 0a = 0C.C.v = 0v = 0, but , but a a ≠≠00D.D.None of the aboveNone of the aboveyExercise 1Exercise 1Motion in One DimensionMotion in One DimensionPage 6Physics 207 – Lecture 3Physics 207: Lecture 3, Pg 11When throwing a ball straight up, which of the following is When throwing a ball straight up, which of the following is true about its velocity true about its velocity vvand its acceleration and its acceleration aaat the highest at the highest point in its path?point in its path?A.A.BothBothv = 0v = 0andanda = 0a = 0B.B.v v ≠≠00, but , but a = 0a = 0C.C.v = 0v = 0, but , but a a ≠≠00D.D.None of the aboveNone of the aboveyExercise 1Exercise 1Motion in One DimensionMotion in One DimensionPhysics 207: Lecture 3, Pg 12In driving from Madison to Chicago, initially my speed is at a In driving from Madison to Chicago, initially my speed is at a constant 65 mph. After some time, I see an accident ahead of me constant 65 mph. After some time, I see an accident ahead of me on on II--90 and must stop quickly so I decelerate increasingly 90 and must stop quickly so I decelerate increasingly ““fastfast””until I until I stop. The magnitude of mystop. The magnitude of myacceleration acceleration vsvstimetimeis given by,is given by,A. B. C. atExercise 2 Exercise 2 More complex Position More complex Position vs.vs.Time GraphsTime Graphs• Question: My velocity vs time graph looks like which of the following ?vtvvPage 7Physics 207 – Lecture 3Physics 207: Lecture 3, Pg 13In driving from Madison to Chicago, initially my speed is at a In driving from Madison to Chicago, initially my speed is at a constant 65 mph. After some time, I see an accident ahead of me constant 65 mph. After some time, I see an accident ahead of me on on II--90 and must stop quickly so I decelerate increasingly fast until90 and must
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