Read and reason
Read the axes before interpreting
A position–time graph puts time t in seconds on the horizontal axis and signed position x in meters on the vertical. If the vertical axis is labeled displacement, it may show x−x₀ instead. Slope equals vertical change divided by horizontal change, (x₂−x₁)/(t₂−t₁); its units are m/s, making it an average velocity over the chosen interval.
The graph can rise and still mean leftward motion
A positive slope corresponds to motion toward increasing position; a negative slope corresponds to decreasing position. This depends on the defined positive direction, not on which way an object appears to move on a screen. If a graph is level while time advances, the position is constant and the object's velocity is zero over that segment. A steep slope is a larger speed magnitude for a straight segment.
Curvature and instantaneous velocity
For a curved position graph, average velocity across two times is the secant slope connecting the two plotted points. Instantaneous velocity at a time is the slope of the tangent at that time in the ideal continuous model. Curvature indicates changing velocity, although the exact value must be established by quantitative calculations. A graph turning upward does not automatically mean a vehicle is physically climbing a hill.
Evaluate the model against data
A line through two points gives a mean slope; extra points can expose curvature or measurement error. If measurements are uncertain, a plausible slope range may be better than a single overly precise value. Record graph units and coordinates used for every calculation. When choosing a model, distinguish an assumption of uniform velocity from empirical evidence that velocity is uniform.