Mechanics Topic 2.1 Kinematics

Kinematics Concepts Displacement is a vector quantity 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 In many situations it is measured from the origin of a Cartesian co-ordinate system

Kinematics Concepts Speed Is the rate of change of distance Or the distance covered per unit time Speed is the total distance (s) covered in total time (t) Speed (v) = total distance (s) total time (t)

Kinematics Concepts Velocity Is the rate of change of displacement Is a measured speed in a given 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

Gradients 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)

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 Ticker tape timers Motion detectors Air tables

The 4 Equations of Uniformly (i.e. constant)Accelerated Motion Aka the “suvat” equations s=displacement u=initial velocity v=final velocity a=acceleration t=time

The 4 Equations Suppose 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 regardless of their masses. This acceleration towards the surface of the Earth, known as the acceleration due to gravity, is denoted by g. Acceleration Due to Gravity

Its magnitude varies slightly from place to place on the Earth´s surface and is approximately 9.81 ms -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 a long enough time, 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 50 ms -1 (100 miles per hour)

Relative Motion If you are stationary and watching things come towards you or away from you, then determining relative velocities is straightforward since your frame of reference is at rest. If, however, you are in motion, either towards or away from an object in motion, then your frame of reference is moving and relative velocities have to be determined from vector addition or subtraction.

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