Mechanics Topic 2.1 Kinematics

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

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)

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

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 small change in the value

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

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´.

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

Gradiants of Graphs Gradiant of a Displacement-time graph is the velocity (instantaneous or average?) Gradiant of a Velocity-time graph is the acceleration (instantaneous or average?)

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

Uniformly Accelerated Motion Velocity and hence Acceleration can be measured using Light gates Strobe photographs ( Duncan Page 142/3) Ticker tape timers

The Equations of Uniformly Accelerated 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

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)

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)

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

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

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

Its magnitude varies slightly from place to place on the Earth´s surface and is approximately 9.8ms -2

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

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.

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.

Terminal velocity depends on The size Shape And weight of the object A sky diver has a terminal velocity of more than 50ms -1 (100 miles per hour)

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

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