In physics, definitions can be expressed mathematically. The definition for speed (and velocity) can be expressed as:
Directions in physics can be assigned positive and negative signs. For now, let right and up be positive and left and down be negative.
In physics, the relationship between variables is examined graphically. If you wanted to experimentally determine the speed (velocity) of an object, you would collect distance (displacement) and time data. Since your distance traveled (or your displacement) depends upon the elapsed time, distance (displacement) is the dependent variable (graphed on the y-axis) and time is the independent variable (graphed on the x-axis). The slope of the line gives the speed (velocity) of the object. On a distance vs time graph, a line of constant slope indicates that the object is moving at constant speed (velocity). A horizontal line (a slope of zero) means that the object is motionless. A curved line (variable slope) means that the speed of the object is changing. On a graph, if a line has positive slope, we say that the object has positive speed (or velocity); if a line has negative slope, we say that the object has negative speed (or velocity).
On a d vs t graph, you can mathematically write the equation for the motion of the object knowing the slope and the y-intercept. Remember, the equation of a line is given as y = mx + b, where m is slope and b is the y-intercept.
Virtual Lab - Horizontal Motion (produces graphs of motion)
Velocity Sample Problems