### SAT Physics Vectors - Coordinate System

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**SAT Physics Vectors - Coordinate System**

Problems in physics often involve the motion of objects. Position, displacement, velocity, and acceleration are key numerical quantities needed to describe the motion of an object. Position involves a specific location, while velocity and acceleration act in specific directions. Using the mathematical **coordinate system**is ideal to visualize both position and direction. The coordinate system provides a common frame of reference in which the quantities describing motion can be easily and consistently compared with one another.

We can place an axis anywhere, and we can orient the axis in any direction of our choosing. If a problem does not specify a starting location or direction, then position the origin at the object’s starting location. In Figure 2.1, a problem involving the motion of a car can be visualized as starting at the origin and moving horizontally along the positive x-axis.

In more complex problems, some quantities cannot be oriented along a common axis. In these problems, direction must be specified in degrees measured counterclockwise (ccw) from the positive x-axis.

A coordinate system is a valuable tool that provides a frame of reference when position and direction are critical factors.

**SCALARS**

A

**scalar**is a quantity having only a numerical value. No direction is associated with a scalar. The numerical value describing a scalar is known as its magnitude. Some examples of commonly used scalars are listed in Table 2.1.

The symbols representing scalars are printed in italics. For example, a mass of 2.0 kilograms will be written as m = 2.0 kg. Scalars can have magnitudes that are positive, negative, or zero. For example, time = 60 seconds, speed = 0 meters per second, and temperature = -10° C.

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