# POSITION & DISPLACEMENT

#### branchMECHANICS (MOTION)

Coming from MECHANICS (MOTION)
Leading to SPEED / VELOCITY
==Position== In most mechanical problems we are asked to determine the connection between speed, position and time. Example - Will two cars crash if they are heading towards each other as they apply brakes at a certain time? To describe the position of a moving object, you have to specify its position relative to a particular point or landmark that is understood by everyone. Along a straight line, you only need the position of the landmark and how far the object is from the landmark left or right (or east or west). 5 metres from the door does not mean anything without giving some indication of direction (inside or out for example). Now left or right is not a good distinction as not everyone can agree with it. In Physics, we specify the origin landmark at 0 and the points either side of it are either positive or negative numbers (in some convenient units). Let us label three positions on such a straight line x~1~, x~2~ and x~3~. [image:https://i.imgur.com/AirA4Wf.png] We shall often want to consider changes in position in our study of motion and we shall give this a special name, ''''DISPLACEMENT''''. If an object moves from position x~1~ to x~2~, its displacement is given by x~2~ – x~1~. That is, the final position minus the initial position. In this case, the '''displacement''' is (3-1) = +2 Displacement can be either a positive or negative number depending on the direction of the change. See what the mathematics has done for us! By defining our space, we have the direction and magnitude of our change in position. Example: x~2~ to x~3~ has a displacement = (-3 - 3) = -6 x~3~ to x~1~ has a displacement = (1 - - 3) = +4 Note how the displacements are independent of the point chosen for the origin of the coordinate line. ==Change== Differences or changes occur so often in science that we have a special symbol to denote this. This is the Greek letter delta Δ. So for a quantity a, Δa means the ‘change in’ a. If you add a time element and made the system dynamic so the position changed with time, the mathematics we would use to track the position with time is called calculus. ==Measuring Position== Displace and Displacement is measured in the standard (SI) unit, Metre The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. In the 1600s this was suggested as the length of a pendulum with a half period of one second. Also one ten-millionth the distance from the equator to the North Pole. A Vernier Calliper and Micrometre are two precise devices commonly used in a laboratory which allow us to distances down to one ten-thousandth of a metre. [image:http://i.imgur.com/0OylXPy.png] Vernier Calliper (Source: http://www.technologystudent.com/) [image:http://i.imgur.com/D4jiXxj.gif] Micrometre (Source: http://www.technologystudent.com/) ==Definitions== '''Distance''' measurements do not have any indication of direction, it is the total length travelled by an object. '''Displacement''' is the length between start and stop positions and includes a direction [image:https://i.imgur.com/z6dsWkX.png] In this example, the '''DISTANCE''' is 110m and the '''DISPLACEMENT''' is 30m North. ==Extra== Circumference of the Earth: Eratosthenes was a Greek astronomer living in Alexandria in the third century BC. He observed that on a certain day of the year, the sun would be directly overhead at around midday and not cast a shadow on a vertical post in Syene, near Aswan. He then travelled 5000 stades south of Alexandria and measured the angle of the shadow cast at the same time to be about a fiftieth of a full circle, about 7 degrees. That means that 50 x 5000 corresponds to a full circle. We do not know the exact dimensions of the stade but modern estimates have this as a few percent low, still good for a man with a stick.
Credit: Ben Himme, Tristan O'Hanlon