HA05-NonLinearGraphing - Non-Linear Graphing Techniques...

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Non -­‐ Linear Graphing Techniques Relationships in Science Physics is the most mathematically driven of the three major sciences. We can even think of physics as the systematic determination of relationships between quantitative observations of nature. Through controlled experiments scientists attempt to determine how a dependent variable changes in response to an independent variable. In physics we initially write these relationships as proportionality statements. - Ex. If you double the force acting on an object, you double the acceleration. This is a direct proportion and is written: ࠵? ࠵? ( means “proportional to”) - Ex. If you double the speed of an object, you quadruple the kinetic energy. We can write this as: ࠵? ࠵? ! - Ex. If the distance to the centre of the Earth doubles, the gravitational force acting on an object is quartered. This can be written as: ࠵? ! ! ! ! From this statement we then try to describe the relationship as a function by introducing constants of proportionality. - Ex. If ࠵? ࠵? then we can write it as a function ࠵? = ࠵?࠵? + ࠵? where a and b are the constants of proportionality It is important to note that by carefully defining units we can choose any constant terms (like b in the last example) to be zero.
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