Determine the equation for the position of the object moving through space. This is most commonly given in a problem, but in real life applications must be experimentally determined. Mathematically, linear equations may be determined using the "point slope" formula and parabolic movement may be determined by solving the zeros of the polynomial and plotting the parabola that connects them. It is important to note that all free falling bodies undergo parabolic trajectories.
Take the first derivative of the position function. The idea of taking its first derivative is such: the rate at which the position changes is equal to the velocity at that particular point in time, as such, the first derivative, or rate of change of the position function, yields the velocity of the object as it moves.
Substitute the time of interest; for example, three seconds after movement started, into the first derivative function. The resulting value is its instantaneous velocity per unit time at that point in its movement. For reference, the first derivative of a function is referred to as and spoken " F prime of x."