Position-time graphs and velocity-time graphs are visualization tools that allow us to describe and understand the motion of a body moving in one dimension. In them, we plot the position (for position-time graphs) or velocity (for velocity-time graphs) of the moving body at a certain time t on the vertical axis against that time t on the horizontal axis.
Although position and velocity are vectors we can plot them as scalars as long as we are careful with their sign because we are considering motion in just one dimension.
To construct a position-time graph, follow these steps:
Step 1: Choose a frame of reference, that is, choose from when and where you will be measuring time and position. A usually convenient choice is to measure time from the instant the motion we want to analyze begins and to measure position from the point where the body is at the beginning of the motion. That way, both our initial time and our initial position will be zero.
Step 2: Draw a cartesian coordinate plane. Each point in the horizontal axis of this cartesian plane will represent an instant in time. Each point in the vertical axis will represent a position along the direction of the motion.
Step 3: Consider a point on the horizontal axis. This point represents a moment t in time. We draw a point whose horizontal coordinate is t, and whose vertical coordinate is the position of the body in our frame of reference at time t. This will be the first point in our position-time graph.
Step 4: We repeat the same process as in Step 3 for each possible point in time. If we know the position of the body at a few moments our graph will consist of a few points, but if we knew the position at each instant, we would end up with a curve made of the infinite succession of points.
To construct a velocity-time graph we follow the same steps, but recording velocity instead of position on the vertical axis.
Figure: Example of position-time graphs for a given motion. The object moves in the positive direction with a speed of 1 m/s for 2 seconds, then stays in place for 3 seconds, and then moves in the negative direction with a speed of 2 m/s for 1 second.