1. Mechanics Topic 2.1 Kinematics

2. Kinematic Concepts: Displacement Is a measured distance in a given direction It is a vector quantity It tells us not only the distance of the object from a particular reference point but also the direction from that reference point Typically, it is measured from the origin of a Cartesian co-ordinate system

3. Kinematic Concepts: Speed Is the rate of change of distance Or is the distance covered per unit time It is a scalar quantity…it has magnitude only Speed is the total distance (d) covered in total time (t) Speed (s) = total distance (d) total time (t)

4. Kinematic Concepts: Velocity Is the rate of change of displacement Is a measured speed in a given direction It is a vector quantity…It tells us not only the speed of the object but also the direction

5. Average Velocity Defined as the total displacement (s) of the object in the total time (t) Velocity (v av ) = total displacement (s) total time (t) v av =  s  t where  indicates a change in the value

6. Instantaneous Velocity Is the velocity at any one instant v =  s  t * Where  t is tending towards zero

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 Acceleration in the same direction as motion results in an increase in speed Acceleration in the opposite direction as motion results in a decrease in speed Acceleration perpendicular to the direction of motion results in a change in direction

8. Graphical Representation of Motion These come in 5 forms… 1. Distance-time graphs 2. Displacement-time graphs 3. Speed-time graphs 4. Velocity-time graphs 5. Acceleration-time graphs

9. Gradiants of Graphs Gradiant of a Displacement-time graph is the velocity Gradiant of a Velocity-time graph is the acceleration

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. The Equations of Uniformly Accelerated Motion There are 4 equations which we use when dealing with constant acceleration problems You need to be able to derive them

12. 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)

13. Since the velocity is increasing steadily, the average velocity is the mean of the initial and final velocities, i.e. Average velocity = u + v 2 If s is the displacement of the body in time t, then since average velocity = displacement/time = s/t We can say s = u + v t 2  s = ½ (u + v) t - equation (2)

14. But v = u + at  s = ½ (u + u + at) t  s = ut + ½at 2 - equation (3)

15. If we eliminate t from (3) by substituting in t = (v – u)/a from (1), we get on simplifying v 2 = u 2 +2as- equation (4) Knowing any three of s, u, v, a, t, and the others can be found

16. 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. Acceleration Due to Gravity

17. Its magnitude varies slightly from place to place on the Earth´s surface and is approximately 9.8ms -2 The IB generally allows for an approximation of 10 ms -1 to be used All of the uniform acceleration equations are applicable to situations of free fall

18. 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

19. 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.

20. If the object falls for long enough, then the air resistance (a force acting upwards) will equal the force of attraction of the Earth (the weight) (a force acting downwards) Now there are no net forces acting on the object (since the two forces balance) so it no longer accelerates, but travels at a constant velocity called its terminal velocity. A sky diver has a terminal velocity of more than 50ms -1 (100 miles per hour)

21. Relative Motion If you are stationary and watching things come towards or away from you, then your stating of velocities is straightforward. If, however you are in motion, either moving towards or away from an object in motion, then your frame of reference is different

22. In this case the relative velocity is the velocity of the object relative to your motion. Common examples include cars overtaking Trains going passed platforms