The most common equation for speed is: speed = distance / time. It can also be expressed as the time derivative of the distance traveled. Mathematically, it can be written as v = s/t, or v = (ds/dt), where speed is denoted by v, distance is denoted by s, and time is denoted by t. In case of uniform velocity, the first equation is used.
Speed is often confused with velocity and is thought to have the same meaning. In terms of physics, speed and velocity are two different things. Speed is a scalar quantity, which means that there is no direction attached with its definition and only represents the magnitude of its velocity. Velocity is a vector quantity and represents both the speed of an object and its direction. For example if a car travels north at 40 miles per hour, then its speed is 40 miles per hour and its velocity is 40 miles per hour to the north.
Speed is associated with the concept of distance, whereas velocity is associated with displacement. Distance, a scalar quantity, represents the length an object has covered during its time of motion. Displacement, a vector quantity, represents how far the object has moved away from its initial position during its time of motion.