Here s is the position of the object, and t is the time. Therefore, the slope of the curve gives the change in position divided by the change in time, which is the definition of the average velocity for that interval of time on the graph. If this interval is made to be infinitesimally small, such that Δ Δ s becomes d s and Δ Δ t becomes d t , the result is the instantaneous velocity at time t , or the derivative of the position with respect to time.