Velocity a particular instant is called instantaneous.
At any point instantaneous velocity acts along the tangent at that point. Mathematically it is measured as the limiting value of the average velocity.
For motion along x – axis,
Initial means, starting time i.e. t = 0
- For 1 D motion along x – axis we have, i.e. instantaneous velocity is equal to slope of position time graph (x – t).
2. On separating the variables & integrating this relation can be rearranged as
i.e. area under x – t graph bounded with the time axis for a time interval is equal to displacement for that time interval.