Kinematics 2011 part1


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Kinematics 2011 part1

  1. 1. flipperworks.comKinematics
  2. 2. flipperworks.comDynam deals with the motion of bodies with icsreference to the forces that act on the system.Kinem atics deals with the motion of bodieswithout reference to the forces that act on thesystem. Two types of motion will be studied: 1. One dimensional motion - rectilinear motion 2. Two dimensional motion - projectile motion
  3. 3. 1. Definition of terms [I] Displacement s Displacem is the distance travelled ent along a specified direction. BBody travels alongcurved path from Ato B. A It is a vector quantity. SI unit: m etre, m
  4. 4.[II] Speed v Speed is the rate of change of distance. It is a scalar quantity. SI unit: m s-1 average speed < v > = total distance covered total time takenA body that travels equal distances in equalintervals of time is said to be moving withc o ns ta nt or unifo rm speed.
  5. 5. flipperworks.comEstimates of speeds (in m s-1) walking 1.5 sprinter 10 Speed limit 25 [ie. 90 km h-1] Jet plane 250 Sound (in air) 330 Light (in vacuum) 3.00 × 108
  6. 6.[III] Velocity v Velocity is the rate of change of displacem ent. It is a vector quantity. SI unit: m s-1 ds v= dt average velocity rate of total displaceme nt change <v > = total time taken
  7. 7. flipperworks.comA body which travels equal distances inthe same direction in equal intervals oftime is said to be moving with c o ns ta ntor unifo rm velocity. < speed > may not always be equal to < velocity >
  8. 8. Example 1: (a) total distance = 5.0 + 5.0 = 10.0 km(b) displacement = 5.0 2 + 5.0 2 N = 7.1 km 5.0 km θ 5 .0 tan θ = = 1 .0 5.0 km 5 .0 ⇒ θ = 45o Displacement is 7.1 km at a bearing of 135 o or S45oE.
  9. 9. 10.0(c) <speed> = 1 .0 = 10 km h-1 7 .1(d) <velocity> = 1.0 = 7.1 km h-1 at a bearing of 135o
  10. 10.[IV] Acceleration a Acceleration is the rate of change of velocity. It is a vector q ua ntity . dv a= SI unit: m s-2 dt A change in velocity can be caused by: (i) a change in its magnitude only, (ii) a change in its direction only, or (iii) a change in both its magnitude and direction.
  11. 11. flipperworks.comA body which travels with equal increasein speed in the same direction in equalintervals of time is said to be movingwith c o ns ta nt or unifo rm acceleration.acceleration = 0 ⇒ constant velocityBut when velocity = 0 at one instant,acceleration need not be zero. (Thinkof a situation where this can happen.)
  12. 12. flipperworks.comRetardation or decelerationdescribes a situation when magnitude ofvelocity decreases with timei.e. body is slowing down.This occurs when acceleration and velocity actin opposite directions.In the next slide, observe the directions of thevelocity and acceleration when a body travelsfaster and when it slows down.
  13. 13. Free fallK A body is said to be in fre e fa ll if the onlyi force acting on it is the gravitational forcee due to the Earth.m The downward acceleration of such a bodya is known as a c c e le ra tio n d ue to g ra vity .t g = 9.81 m s-2c (assumed to be constant near Earth’s surface)s True free fall only occurs in vacuum. All bodies falling freely will have this constant acceleration regardless of their masses.
  14. 14. 2 Graphical Representation of MotionK 2.1 Displacement-time graphin displacement , s average velocity between O and A = S1e t1 s1m A (gradient of the linea passing through O & A)ts time, t O t1
  15. 15. flipperworks.comdisplacement , s slope at A = s1 A ds instantaneous velocity at A ds dt = dt time, t O t1
  16. 16. x constant ⇒ body is stationaryx or velocity is zero A B x decreases at a constant rate ⇒ body is moving back towards O. Velocity is negative, uniform and greater in magnitude than t that of OA.0 x increases at a constant rate C ⇒ body is moving with uniform velocity xO A
  17. 17. flipperworks.comExamples of displacement-time graphs(a) s t uniform velocity (constant gradient)
  18. 18. flipperworks.comExamples of displacement-time graphs(b) s curve 1 t Curve 1: increasing velocity (gradient increasing)
  19. 19. flipperworks.comExamples of displacement-time graphs(b) s curve 2 t Curve 2: decreasing velocity (gradient decreasing)