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UW-Madison PHYSICS 207 - Lecture 3

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Physics 207, Lecture 3, Sept. 10Position, velocity & acceleration for motion along a linePosition, displacement, velocity & accelerationAnd given a constant acceleration we can integrate to get explicit vx and axSlide 5Rearranging terms gives two other relationshipsAccelerationAcceleration has its limitsFree FallWhen throwing a ball straight up, which of the following is true about its velocity v and its acceleration a at the highest point in its path?Slide 11In driving from Madison to Chicago, initially my speed is at a constant 65 mph. After some time, I see an accident ahead of me on I-90 and must stop quickly so I decelerate increasingly “fast” until I stop. The magnitude of my acceleration vs time is given by,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 on I-90 and must stop quickly so I decelerate increasingly fast until I stop. The magnitude of my acceleration vs time is given by,Gravity facts:Gravity Map of the Earth (relief exaggerated)Gravity map of the USExercise 3 1D FreefallSlide 18Problem Solution Method:Example of a 1D motion problemThe pictureUsingSlide 24Now Algebra and Relationship 4FiniTips:See you MondayPhysics 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 1-dimensional velocity & acceleration in systems with 1-dimensional motion and non-zero acceleration (usually constant)motion and non-zero acceleration (usually constant) Solve problems with zero and constant acceleration Solve problems with zero and constant acceleration (including free-fall and motion on an incline)(including free-fall and motion on an incline) Use Cartesian and polar coordinate systemsUse Cartesian and polar coordinate systems Perform 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 vx and instantaneous acceleration ax as a function of time!vxtxtaxt22vadtxddtdxxdtdxxv] offunction a is [ )( txtxx Physics 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)vaPhysics 207: Lecture 3, Pg 4And given a And given a constant accelerationconstant acceleration we we can integrate to get explicit can integrate to get explicit vvxx and and aaxxxaxvxttttxxx avv02210 a v0ttxxxxconsta x22vadtxddtdxxdtdxxv] offunction a is [ )( txtxx 0x0Physics 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 xaxtPhysics 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 simultaneouslyvv11vv00vv33vv55vv22vv44aa aa aa aa aa aa vatt0v(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 photoPhysics 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 vv and its and its acceleration acceleration aa at the highest point in its path? at the highest point in its path?A.A.BothBoth v = 0v = 0 andand a = 0a = 0B.B.v v  0 0, but , but a = 0a = 0C.C.v = 0v = 0, but , but a a  0 0D.D.None of the aboveNone of the aboveyExercise 1Exercise 1Motion in One DimensionMotion in One DimensionPhysics 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 vv and its acceleration and its acceleration aa at the highest at the highest point in its path?point in its path?A.A.BothBoth v = 0v = 0 andand a = 0a = 0B.B.v v  0 0, but , but a = 0a = 0C.C.v = 0v = 0, but , but a a  0 0D.D.None of the aboveNone of the aboveyExercise 1Exercise 1Motion in One DimensionMotion in One DimensionPhysics 207: Lecture


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UW-Madison PHYSICS 207 - Lecture 3

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