Describing Motion

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Many of the objects we encounter in everyday life are in motion or have parts that are in motion.  Motion is the rule, not the exception.  The physical laws that govern the motion of these objects are universal, i.e. all the objects move according to the same rules.

When an object moves, its position changes as a function of time.  A change in position is called a displacement.  The position of an object is given relative to some agreed upon reference point.  It is not enough to just specify the distance from the reference point.  We also have to specify the direction.  Distance is a scalar quantity, it is a number given in some units.  Position is a vector quantity.  It has a magnitude as well as a direction.  The magnitude of a vector quantity is a number (with units) telling you how much of the quantity there is and the direction tells you which way it is pointing.  In text, vector quantities are usually printed in boldface type or with an arrow above the symbol.  Thus, while d = distance, d = displacement.

A convenient way to represent a vector object in a drawing is to use a straight line with an arrowhead at one end.  The length of the line is scaled according to the magnitude and the arrow shows the direction of the vector. 

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Vectors can be added graphically by lining up the arrows tail to tip.  The sum is the arrow drawn from the tail of the first vector to the tip of the last vector. 

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Vector quantities can be separated into components.  The components are often chosen to point along the directions of the axes of a coordinate system.  The components of a vector add up to form the vector itself.


Problem:

While traveling along a straight interstate highway you notice that the mile marker reads 260.  You travel until you reach the 150-mile marker, and then retrace your path to the 175-mile marker.  What is the magnitude of your resultant displacement from the 260-mile marker?