The mathematical description of motion, or kinematics, is based on the idea of specifying positions using numerical coordinates. Movement is represented by these numbers changing over time: a body's trajectory is represented by a function that assigns to each value of a time variable the values of all the position coordinates. The simplest case is one-dimensional, that is, when a body is constrained to move only along a straight line. Its position can then be given by a single number, indicating where it is relative to some chosen reference point. For example, a body might be free to slide along a track that runs left to right, and so its location can be specified by its distance from a convenient zero point, or origin, with negative numbers indicating positions to the left and positive numbers indicating positions to the right. If the body's location as a function of time is s ( t ) , then its average velocity over the time interval from t 0 to t 1 is Δ Δ s Δ Δ t = s ( t 1 ) − − s ( t 0 ) t 1 − − t 0 . Here, the Greek letter Δ Δ (delta) is used, per tradition, to mean "change in". A positive average velocity means that the position coordinate s increases over the interval in question, a negative average velocity indicates a net decrease over that interval, and an average velocity of zero means that the body ends the time interval in the same place as it began. Calculus gives the means to define an instantaneous velocity, a measure of a body's speed and direction of movement at a single moment of time, rather than over an interval. One notation for the instantaneous velocity is to replace Δ Δ with the symbol d , for example, v = d s d t . This denotes that the instantaneous velocity is the derivative of the position with respect to time. It can roughly be thought of as the ratio between an infinitesimally small change in position d s to the infinitesimally small time interval d t over which it occurs. More carefully, the velocity and all other derivatives can be defined using the concept of a limit. A function f ( t ) has a limit of L at a given input value t 0 if the difference between f and L can be made arbitrarily small by choosing an input sufficiently close to t 0 . One writes, lim t → → t 0 f ( t ) = L . Instantaneous velocity can be defined as the limit of the average velocity as the time interval shrinks to zero: d s d t = lim Δ Δ t → → 0 s ( t + Δ Δ t ) − − s ( t ) Δ Δ t . Acceleration is to velocity as velocity is to position: it is the derivative of the velocity with respect to time. Acceleration can likewise be defined as a limit: a = d v d t = lim Δ Δ t → → 0 v ( t + Δ Δ t ) − − v ( t ) Δ Δ t . Consequently, the acceleration is the second derivative of position, often written d 2 s d t 2 .