Graph of uniform motion

Graph of uniform motion

the motion

This is one of the most important applications, which gives interpretation of the equation of a straight line and its coefficients. If the point P moves along a certain path (trajectory), its position is fully defined by the distance, measured from either side along the trajectory from a given point A of it to the point P. This distance, i.e. the arc AP, is called the path traversed, and is denoted by the letter s; s can be both positive and negative, its values on one side of the initial point A being reckoned positive, and on the other side, negative.

The path s traversed is a certain function of time t taking time as the independent variable, we can draw a graph of the motion, i.e. a graph of the functional relationship (Fig. 9):

uniform motion

this is not to be confused with the trajectory itself. The motion is called uniform if the path traversed by a point in any given interval of time is proportional to this interval, in other words, if the ratio

of the path traversed in the interval from tl to t2, to the size of this interval, is a constant; this constant is called the velocity of the motion and is denoted by v It is clear from the above that the equation of the graph of uniform motion has the form:

the graph itself is a straight line, the slope of which is equal to the velocity whilst the initial ordinate s0 is the initial value of the path s traversed, i.e. the value of s at t = 0. Figure 10 shows the graph of the motion of a point P, moving with constant velocity v1 in a positive direction from the instant 0 to the instant t1 (acute angle with axis of t), then with higher constant velocity v2 in the same direction (larger acute angle) to the instant t2, then with negative constant velocity v3 (in the opposite direction, obtuse angle) back to its initial position.

 the source:

A COURSE OF Higher Mathematics VOLUME I. SMIRNOV.

By: Fady tarek