Final answer:
On a velocity-time graph, time is plotted on the x-axis as the independent variable, and velocity is plotted on the y-axis as the dependent variable. The slope of the graph signifies acceleration, while the y-intercept represents the initial velocity.
Step-by-step explanation:
In a velocity-time graph, the axis typically represents different variables that describe motion. The horizontal axis, or x-axis, displays the independent variable which in the context of a velocity-time graph is time. This is because time is the variable that other quantities, such as velocity, depend upon. Consequently, time is plotted on the x-axis. The vertical axis, or y-axis, shows the dependent variable which is velocity in a velocity-time graph. This arrangement is because velocity is the quantity that changes in response to the passage of time. The slope of the line on this type of graph represents acceleration, and the y-intercept signifies the initial velocity.
For example, if we have a graph depicting the motion of a jet-powered car on a flat dry lake bed in Nevada with constant velocity, indicated by a straight line with zero slope (as acceleration is zero), time would be on the x-axis and velocity would be on the y-axis. This is reflective of the concept that while velocity can change as time progresses, time itself does not depend on the velocity of the object but rather proceeds uniformly forward. Also, motions along perpendicular axes are independent, affirming why we plot time and velocity on different axes.
It is important to note that on some graphs, you may encounter negative values for velocity, indicating motion in the opposite direction. However, negative time is not reasonable in physical graphs, as time is always progressing forward.