Mechanics

# Time equation of spaces

In some types of motion it is possible to determine a mathematical law that relates time to the position of the mobile, that is, to its abscissa in the trajectory. Evidently, for each value of t there will be a unique abscissa s indicative of its position on the trajectory.

However, the opposite may not be true, since a piece of furniture may pass through an abscissa several times, at different times, in addition to being able to stand still for some time on a given abscissa.

There are some simple movements in which a correspondence between s and t can be obtained , which can be translated into an equation, which we will call the clockwise equation of spaces or abscissa . Let’s look at some cases:

Movement whose clockwise equation is of the 1st degree in t :

S = 4 – 2t (SI units)

S = – 5 + 3t (SI units)

Movement whose clockwise equation is of the 2nd degree in t :

S = 2 + 3t – 5t 2 ( SI units)
S = 7t – 2t 2 (SI units)

In this way, we can say that from these equations, that is, through the time equations of spaces, we can discover the position of the mobile on a trajectory at any moment of the movement. Let’s look at an example:

Let’s consider a movement that obeys the following time equation of spaces with SI units:

S = 6t – 12

Find the space at time t = 3s

S=6t-12
S=6.(3)-12
S=6 m