Time is an abstract entity (as well as a physical quantity), useful for quantifying and measuring the passing of events. The most fundamental physical quantities are defined by how they are measured. This is the case with time. Every measurement of time involves measuring a change in some physical quantity. It may be a number on a digital clock, a heartbeat, or the position of the Sun in the sky. In physics, the definition of time is simple — time is change or the interval over which change occurs. It is impossible to know that time has passed unless something changes.
The amount of time or change is calibrated by comparison with a standard. The SI unit for time is the second, abbreviated s. This allows us to not only measure the amount of time but also to determine a sequence of events.
How does time relate to motion? We are usually interested in elapsed time for a particular motion. To find the elapsed time, we note the time at the beginning and end of the motion and subtract the two. Elapsed time \(\Delta t\) is the difference between the ending time and beginning time:
where \(\Delta t\) is the change in time or elapsed time, \(t_f\) is the time at the end of the motion, and \(t_0\) is the time at the beginning of the motion. (As usual, the delta symbol, \(\Delta\), means the change in the quantity that follows it). Life is simpler if the beginning time \(t_0\) is taken to be zero. If \(t_0=0\), then:
\[\Delta t=t_f\equiv t\]