### SAT Physics Conventions and Graphing - Interpreting Graphs

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SAT Physics Conventions and Graphing - Interpreting Graphs

Consider the graph of velocity versus time in Figure 1.2.The graph tells the story of an object, such as a car, as it moves over a 60-second period of time. At time zero, the object has a velocity of 0 meters per second and is therefore starting from rest. The y-intercept of a speed versus time graph is the initial velocity of the object, v

_{0}.

What the object is doing during the 60 seconds can be determined by analyzing the slope and area during the separate time intervals. Determine the significance of the slope by dividing the rise units (y-axis values) by the run units (x-axis values).

The slope units, meters per second squared (m/s

^{2}), are the units of acceleration. Thus, the slope of speed versus time is acceleration. Determine the significance of the area between the graphed function and the x-axis by multiplying the units of the y-axis by the units of the x-axis.

area units = height units X base units = m/s x s = m

Meters (m) are the units of displacement. The area of a velocity versus time graph is displacement.

To analyze the motion mathematically, divide the graph into a series of line segments and evaluate each section. The following chart shows the acceleration and displacement for the time intervals corresponding to the graphed line segments.

**Graphs That Illustrate Physics Equations**

The SAT Subject Test in Physics may ask you to identify which graph correctly matches a given equation. Equations in beginning physics typically take one of four possible forms: linear, quadratic, square root, and inverse. You can quickly deduce the shape of a graph by looking at the relationship between the dependent and independent variables as shown in Table 1.3.
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