2.1 Kinematics


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2.1 Kinematics

  1. 1. MechanicsTopic 2.1 Kinematics
  2. 2. Kinematic Concepts Displacement Is a measured distance in a given direction It tells us not only the distance of the object from a particular reference point but also the direction from that reference point It is a vector quantity In many situations it is measured from the origin of a Cartesian co-ordinate system
  3. 3. Kinematic Concepts Speed Is the rate of change of distance Or the distance covered per unit time Speed is the total distance (d) covered in total time (t) Speed (s) = total distance (d) total time (t)
  4. 4. Kinematic Concepts Velocity Is the rate of change of displacement Is a measured speed in a given direction It tells us not only the speed of the object but also the direction It is a vector quantity
  5. 5. Average Velocity Defined as the total displacement (s) of the object in the total time (t) Velocity (vav) = total displacement (s) total time (t) vav = ∆s ∆t Where ∆ indicates a small change in the value
  6. 6. Instantaneous Velocity Is the velocity at any one instant v = ∆s ∆t Where ∆t is tending towards zero
  7. 7. Kinematic Concepts Acceleration Is the rate of change of velocity in a given direction a = ∆v / ∆t (where ∆v = v – u) It is a vector quantity If the acceleration of an object is positive then we understand its rate of change of velocity to be positive and it could mean that its speed is increasing  Do not think of acceleration as a ´slowing up´or a ´getting faster´.
  8. 8. Graphical Representation of MotionThese come in 4 forms1. Distance-time graphs2. Displacement-time graphs3. Velocity-time graphs4. Acceleration-time graphs
  9. 9. Gradiants of Graphs Gradient of a Displacement-time graph is the velocity (instantaneous or average?) Gradient of a Velocity-time graph is the acceleration (instantaneous or average?)
  10. 10. Areas Under Graphs Area under a Velocity-time graph is the displacement Area under a Acceleration-time graph is the velocity Areas can be calculated by the addition of geometric shapes
  11. 11. Uniformly Accelerated Motion Velocity and hence Acceleration can be measured using  Light gates  Strobe photographs ( Duncan Page 142/3)  Ticker tape timers
  12. 12. The Equations of UniformlyAccelerated Motion There are 4 equations which we use when dealing with constant acceleration problems I call them the “suvat” equations You need to be able to derive them
  13. 13. The 4 Equations Supposing the velocity of a body increases from u to v in time t, then the uniform acceleration, a is given by a = change of velocity time taken a=v–u t ∴ v = u + at - equation (1)
  14. 14. Since the velocity is increasing steadily, theaverage velocity is the mean of the initial andfinal velocities, i.e.Average velocity = u + v 2If s is the displacement of the body in time t,then since average velocity =displacement/time = s/tWe can say s = u + v t 2∴ s = ½ (u + v) t - equation (2)
  15. 15. But v = u + at ∴ s = ½ (u + u + at) t∴ s = ut + ½at2 - equation (3)
  16. 16. If we eliminate t from (3) bysubstituting in t = (v – u)/a from (1),we get on simplifyingv2 = u2 +2as - equation (4)Knowing any three of s, u, v, a, t, andthe others can be found
  17. 17. Acceleration Due to Gravity Experiments show that at a particular place all bodies falling freely under gravity, in a vacuum or where air resistance is negligible, have the same constant acceleration irrespective of their masses. This acceleration towards the surface of the Earth, known as the acceleration due to gravity, is donated by g.
  18. 18. Its magnitude varies slightly from placeto place on the Earth´s surface and isapproximately 9.8ms-2
  19. 19. The Effects of Air Resistance Air resistance depends on 2 things  Surface area  Velocity Air resistance increases as surface area increases Air resistance increases as the velocity increases
  20. 20. Terminal Velocity As an object falls through the air, it accelerates, due to the force of attraction of the Earth. This force does not change. As the velocity increases, the air resistance, the force opposing the motion, increases, therefore the acceleration decreases.
  21. 21. If the object falls for long enough, then theair resistance (a force acting upwards) willequal the force of attraction of the Earth (theweight) (a force acting downwards)Now there are no net forces acting on theobject (since the two forces balance) so it nolonger accelerates, but travels at a constantvelocity called its terminal velocity.
  22. 22. Terminal velocity depends on The size Shape And weight of the objectA sky diver has a terminal velocity of morethan 50ms-1 (100 miles per hour)
  23. 23. Relative Motion If you are stationary and watching things come towards you or away from you, then your stating velocities is easy. If, however you are in motion, either moving towards or away from an object in motion, then your frame of reference is different
  24. 24. In this case the relative velocity is thevelocity of the object relative to yourmotion.Examples include cars overtaking Trains going passed platforms