Final answer:
The presence of a constant rate of change between two quantities typically signals a linear relationship, often represented by the equation y = mx + b. For the jet car's motion, the relationship is not linear while the acceleration changes, but becomes linear once the acceleration is zero and the velocity becomes constant. The linear part of the graph would show a straight line from which the rate of change can be determined using the slope formula.
Step-by-step explanation:
To determine if the relationship between two quantities is linear, one should look at the rate of change between the variables. If the rate of change is constant, meaning the same amount is added to one variable in response to a set increase in the other variable, the relationship is linear. The equation for a linear relationship is often written as y = mx + b, where m represents the slope, or rate of change, and b represents the y-intercept.
In the context of graphing physical quantities, as is common in physics and sciences, if a graph shows a straight line, this indicates a linear relationship with its slope representing the rate of change. If a graph does not depict a straight line, the relationship is not linear, and the rate of change is not constant. Examples of non-linear graphs include quadratic, inverse, and exponential relationships.
To find the constant rate of change for a linear relationship, one could use the slope formula, m = (y2 - y1) / (x2 - x1), by selecting two points on the graph. For the provided graph showing the motion of a jet car, it is noted that until time t = 55 s, the slope of the graph increases, meaning acceleration is not constant. After 55 seconds, when acceleration decreases to zero, the relationship becomes linear since the velocity remains constant from that point onward, and the graph would show a straight line. During the time when the acceleration is zero, the slope of the velocity-time graph would represent the constant rate of change.