I actually wanted to understand calculus. And read many a times, that concept of differentiation is about splitting the path into infinitesimally small divisions. In most cases the such division is difficult manually, because paths are random. But what if the path is perfect circle in shape ? That brought me up with this question.
Here is a velocity time graph, such that, it draws a perfect arc, with a center at "o" and radius "r". The length of arc is say, "m". I want to calculate the the velocity at point "p". Can i calculate the velocity by simple math but without the help of calculus or drawing any tangent there on the point ?
Thnx.
Unless you invented time travel, that cannot be a velocity-time graph, since the graph curls up over itself so that there are two values of $v$ for some values of $t$.
But if we remove that offending part of the graph to the upper right, your question is extremely simple. In a velocity-time graph, velocity is the $y$-coordinate. So, the velocity at point "p" is simply the $y$-coordinate of point "p".
Did you mean that to be a position-time graph?