Final answer:
A graph that is linear represents a direct proportionality and should be a straight line, not curved. In physics, the displacement vs time graph for constant acceleration is curved, whereas the displacement vs time squared graph is linear and straight. The slope of a curve on such a graph can reveal information like velocity at a given time.
Step-by-step explanation:
Understanding the Nature of Graphs in Physics
When approaching the concept of graphing in physics, it's important to understand the relationship between the variables represented. In the context of motion, a graph that is linear does not have a curved line. By definition, a linear graph represents a relationship of direct proportionality between two variables, typically described by the equation y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.
For a motion where an object is moving with constant acceleration, the displacement vs time graph will exhibit a curved line because the rate of change of displacement (which is velocity) is changing. However, when displacement is plotted against time squared, this relationship becomes linear, resulting in a straight line because the acceleration (the rate of change of velocity) is constant. This underscores why the position vs time graph of an object that is speeding up cannot be a straight line, since a straight line would imply constant velocity, not constant acceleration.
To determine characteristics such as velocity from a graph, one can take the slope of the curve at a given point in time. As an example, the slope of a displacement vs time graph at a certain time can reveal the velocity of an object at that time. A linear graph in various fields, such as economics, can effectively represent the relationship between two changing variables, like unemployment rate over time or prices and quantities in the market.
In summary, whether a graph is linear with a straight line or curved depends on the nature of the relationship between the plotted variables and the consistency of the rate of change of the dependent variable.