VELOCITY AND ACCELERATION IS EXPRESSED IN TERM OF TIME (t)

Although velocity is defined as the rate of change of position, it is often common to start with an expression for an object's acceleration. As seen by the three green tangent lines in the figure, an object's instantaneous acceleration at a point in time is the slope of the line tangent to the curve of a v(t) graph at that point. In other words, acceleration is defined as the derivative of velocity with respect to time:

${\displaystyle {\boldsymbol {a}}={\frac {d{\boldsymbol {v}}}{d{\mathit {t}}}}.}$

From there, we can obtain an expression for velocity as the area under an a(t) acceleration vs. time graph. As above, this is done using the concept of the integral:

${\displaystyle {\boldsymbol {v}}=\int {\boldsymbol {a}}\ d{\mathit {t}}.}$