Acceleration at a particular instant of time is called instantaneous acceleration. Mathematically it is measured as the limiting value of the average acceleration.
For motion along x – axis,=
For 1 D motion along x – axis we have,
i.e. instantaneous acceleration is equal to slope of velocity time graph (v – t).
On separating the variables & integrating this relation can be rearranged as
i.e. area under v – t graph bounded with the time axis for a time interval is equal to change in velocity for that time interval.
i.e. instantaneous acceleration is slope of velocity time graph (v – t) or velocity times slope of v – x graph.