Motion in one dimension


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Motion in one dimension

  1. 1. Kinematics in One DimensionChapter 2
  2. 2. Kinematics deals with the concepts thatare needed to describe motion.Dynamics deals with the effect that forceshave on motion.Together, kinematics and dynamics formthe branch of physics known as Mechanics.
  3. 3. 2.2 Speed and VelocityQuestion 1: Explain the meaning of speed using yourown words.2118100510152025Incorrect Partially correct Incorrect20 20 200510152025Correct Partially Incorrect
  4. 4. 2.2 Speed and VelocityQuestion 2: Is the 257 km/h he was caught drivingan average or instantaneous speed?.1139051015202530354045Average Instantaneous50100102030405060Instantaneous Average
  5. 5. 2.2 Speed and VelocityQuestion 4: Do you think that speed kills?3231505101520253035It Kills It Doesnt It Depends3182105101520253035Kills It does nt It dependsSeries1
  6. 6. 2.1 Displacementpositioninitialoxpositionfinalxntdisplacemeoxxx
  7. 7. 2.2 Average Speed and VelocityAverage speed is the total distance traveled divided by the timerequired to cover the distance.timeTotalDistanceTotalspeedAverageSI units for speed: meters per second (m/s)Mathematically it meansNote: The emphasis of on the total distance covereddivided total time taken
  8. 8. 2.2 Speed and VelocityExercise: Distance Run by a JoggerHow far does a jogger run in 1.5 hours (5400 s) if hisaverage speed is 2.22 m/s?timeElapsedDistancespeedAveragem12000s540022.2timeElapsedspeedAverageDistancesm
  9. 9. 2.2 Speed and VelocityAverage velocity is the displacement divided by the elapsedtime.timeElapsedntDisplacemevelocityAveragettt oo xxxvNote: The emphasis of on the displacement dividedchange in time
  10. 10. 2.2 Speed and VelocityExercise: The World’s Fastest Jet-Engine CarAndy Green in the car set a world record of 341.1 m/s in 1997. Toestablish such a record, the driver makes two runs through thecourse, one in each direction to nullify wind effects. From thedata, determine the average velocity for each run.
  11. 11. 2.2 Speed and Velocitysm5.339s4.740m1609txvsm7.342s4.695m1609txv
  12. 12. 2.2 Instantaneous Speed and VelocityThe instantaneous velocity indicates how oftenan object changes position and the directionof motion at eachinstant of time.ttxv0lim
  13. 13. Speed versus Velocity• Speed is associated with distance whilevelocity is associated with displacement• Change in velocity means that:1)The magnitude of velocity changes or/and2)The direction of an object changes• If motion is in one dimension, themagnitude and direction of speed is thesame as that of velocity, that’s why theycan be used interchangeably
  14. 14. 2.3 AccelerationThe notion of acceleration emerges when a change invelocity is combined with the time during which thechange occurs.Acceleration measures how often the velocitychanges with respect to time.The average acceleration is then given by:ttt oo vvva
  15. 15. 2.3 AccelerationExample 3 Acceleration and Increasing VelocityDetermine the average acceleration of the plane.sm0ovhkm260vs0ot s29tshkm0.9s0s29hkm0hkm260oottvva
  16. 16. 2.3 Acceleration
  17. 17. 2.3 AccelerationExample 3 Acceleration and DecreasingVelocity2sm0.5s9s12sm28sm13oottvva
  18. 18. 2.3 Acceleration
  19. 19. For you to doAt one instant of time, a car and a truck are traveling side byside in adjacent lanes of a highway. The car has a greatervelocity than the truck has. Does the car necessarily havethe greater acceleration?A. YesB. NoExplanation
  20. 20. Two cars are moving in the same direction (the positivedirection) on a straight road. The acceleration of each caralso points in the positive direction. Car 1 has a greateracceleration than car 2 has. Which one of the followingstatements is true?A. The velocity of car 1 is always greater than the velocity of car 2.B. The velocity of car 2 is always greater than the velocity of car 1.C. In the same time interval, the velocity of car 1 changes by a greateramount than the velocity of car 2 does.D. In the same time interval, the velocity of car 2 changes by a greateramount than the velocity of car 1 does.
  21. 21. 2.4 Equations of Kinematics for Constant AccelerationIt is customary to dispense with the use of boldface symbolsoverdrawn with arrows for the displacement, velocity, andacceleration vectors. We will, however, continue to conveythe directions with a plus or minus sign.oottvvaoottxxvoottxxvoottvva
  22. 22. Your TurnA car is traveling along a straight road and is decelerating.Which one of the following statements correctly describesthe car’s acceleration?(a) It must be positive.(b) It must be negative.(c) It could be positive or negative.Answers (a) and (b) are incorrect.The term “decelerating” means only that the acceleration vector points opposite to the velocity vector.It is not specified whether the velocity vector of the car points in the positive or negative direction.Therefore, it is not possible to know whether the acceleration is positive or negative.Answer (c) is correct.The acceleration vector of the car could point in the positive or the negative direction, so thatthe acceleration could be either positive or negative, depending on the direction in which the caris moving.
  23. 23. Your TurnWhen an object moves with constant acceleration, itsvelocity…A: IncreasesB: DecreasesC: remains constantD: Both A and B can be correct
  24. 24. 2.4 Equations of Kinematics for Constant Accelerationoottxxv0ox 0ottvvtvx o21Let the object be at the origin when the clock starts.txv
  25. 25. 2.4 Equations of Kinematics for Constant Accelerationoottvvatvva oovvatatvv o
  26. 26. 2.4 Equations of Kinematics for Constant Accelerationatvv otatvvtvvx ooo 2121221attvx o
  27. 27. 2.4 Equations of Kinematics for Constant Accelerationavvvvtvvx ooo 2121tvva oavvt oavvx o222
  28. 28. 2.4 Equations of Kinematics for Constant AccelerationEquations of Kinematics for Constant Accelerationtvvx ox 2102210)( attvx oxatvv o)(2 022xxavv o
  29. 29. 2.5 Applications of the Equations of KinematicsReasoning Strategy1. Make a drawing.2. Decide which directions are to be called positive (+) andnegative (-).3. Write down the values that are given for any of the fivekinematic variables.4. Select the appropriate equation.5. When the motion is divided into segments, remember thatthe final velocity of one segment is the initial velocity for the next.6. Keep in mind that there may be two possible answers to akinematics problem.
  30. 30. 2.4 Equations of Kinematics for Constant Accelerationm110s0.8sm0.2s0.8sm0.62221221attvx o
  31. 31. 2.4 Equations of Kinematics for Constant AccelerationExample 6 Catapulting a Jet: Find its displacement.sm0ov ??x2sm31a sm62vm62sm312sm0sm622 22222avvx o
  32. 32. 2.5 Applications of the Equations of KinematicsActivity: Physics and the Construction IndustryYou are designing an airport for small planes. One kind of theplane that might use the airfield must reach a speed before atakeoff of at least 27.8 m/s. and can accelerate at a 2.00 m/s2.(a) If the runway is 150m long, do you think the airplane canreach the required speed for takeoff? (b) If not, what minimumlength must the runway have?x a v vo t150 m 2 m/s2 ? 27.8 m/s
  33. 33. A ball is thrown vertically upwards from the surface of the earth.Consider the following quantities based on the motion of the ball.(1) Speed; (2) velocity; (3) accelerationQuestion 1 : Speed, velocity and acceleration1.1 Which of these is (are) zero when the ball has reached the maximumheight at point C? Give reasons for your answer.A: 1 and 2 only, B: 1 and 3 only, C: 1 only, D: 2 only, E: 1, 2 and 3Reason:1.2 What do you think will be the magnitude and direction of acceleration ofan object at the following points? Say : Increase , decrease and remainconstant , for direction down is positive up negative Give reasons for youranswer.1.2.1 A 1.2.2 B 1.2.3 C 1.2.4 D 1.2.5 E1.3 What do you think will happen to the velocities of an object at thefollowing points? (Only say, increase, decrease, zero or remains the sameand give reasons)1.3.1 A 1.3.2 B 1.3.3 C 1.3.4 D 1.3.5 EReason:
  34. 34. Question 2: The case of two objects withdifferent massesIf two objects, one with BIGGER mass and the otherwith SMALLER mass are made to fall from the sameheight, Which one do you think it will reach the groundfirst?A: Object with bigger massB: Object with smaller massC: They will reach the ground at the sameExplanation
  35. 35. Question 3Does the pellet in part b strike the ground beneath the cliffwith a smaller, greater, or the same speed as the pelletin part a?
  36. 36. 2.6 Freely Falling BodiesGenerally, during the absence of air resistance, it is foundthat all bodiesat the same location above the Earth fallvertically with the same acceleration.If the distance of the fall is small compared to the radius ofthe Earth, then the acceleration remains essentiallyconstant throughout the descent.This idealized motion is called free-fall and the accelerationof a freely falling body is called the acceleration due togravity.sm80.9 2g
  37. 37. 2.4 Equations of Kinematics for Constant AccelerationEquations of Kinematics for Constant Accelerationtvvx ox 2102210)( attvx oxatvv o)(2 022xxavv o
  38. 38. 2.4 Equations of Kinematics for Constant AccelerationEquations of Kinematics for Constant Accelerationtvvy oy 2102210)( gttvy oygtvv o)(2022yygvv o
  39. 39. ConventionsObject moving up : velocity/speed is negativeObject moving down: velocity/speed is positive
  40. 40. 2.6 Freely Falling Bodies2sm80.9g
  41. 41. About the MCQ Test271421132405101520250 to 4 5 to 7 8 to 9 10 to 11 12 to14 15 to 16 17 and aboveActualNumberofStudentsPS1AFET Test 1 Scores Distribution 2013Only 30% which is 19 out of 63 passed
  42. 42. 2.6 Freely Falling BodiesA Falling Stone:A stone is dropped from the top of a tall building. After 3.00sof free fall, what is the displacement y of the stone?Let the downwardsmotion be positivey g v vo t? 9.80m/s20m/s3.0 sm1.44s00.3sm80.9s00.3sm022212210gttvy oy
  43. 43. 2.6 Freely Falling BodiesHow High Does it Go?The referee tosses the coin upwith an initial speed of 5.00m/s.In the absence if air resistance,how high does the coin go aboveits point of release?y g v vo t? -9.80 m/s2 0 m/s +5.00m/s
  44. 44. 2.6 Freely Falling Bodies)(222yoo ygvvgvvyy o2220m28.1sm80.92sm00.5sm02 222220gvvyy o
  45. 45. 2.6 Freely Falling BodiesConceptual Example 14 Acceleration Versus VelocityThere are three parts to the motion of the coin. On the wayup, the coin has a vector velocity that is directed upward andhas decreasing magnitude. At the top of its path, the coinmomentarily has zero velocity. On the way down, the coinhas downward-pointing velocity with an increasing magnitude.In the absence of air resistance, does the acceleration of thecoin, like the velocity, change from one part to another?
  46. 46. Test your Knowledge1. A sandbag is dropped from a height of 150 m, from a hot airballoon that is moving upwards with a velocity of 5.0 ms-1. Ignoreair resistance.a) What is the initial velocity of the sandbag?b) How long will the bag take to reach the ground?2. A bicycle’s brakes can produce a deceleration of 2.5 ms-2. How farwill the bicycle travel before stopping, if it is moving at 10 ms-1when the brakes are applied?3. Starting from a dead stop at the bottom of the on-ramp it can beassumed that John accelerates at a rate of 6.7 m/s2. How long doesit take for John to reach a speed of 30m/s? How far has Johntravelled in this time if you take his starting point to be 0m?4. Baseball pitcher Josh Beckett throws a ball straight up in the air, theballs mass is 4kg, and he releases it at a speed of 35m/s, what isthe maximum height that the ball will reach, and how long will it takefor the ball to come back down and hit the ground next to him?Assume there is no air resistance, and the ball is released from andreturns to a level of 0m.Prescribed book Ch 2 no 9 to 11; 28, 34, 41, 57 & 62
  47. 47. 2.7 Graphical Analysis of Velocity and Accelerationsm4s2m8Slopetx
  48. 48. 2.7 Graphical Analysis of Velocity and Acceleration
  49. 49. 2.7 Graphical Analysis of Velocity and Acceleration
  50. 50. 2.7 Graphical Analysis of Velocity and Acceleration2sm6s2sm12Slopetv