How To Find Distance On Position Time Graph

It was learned before in Lesson three that the slope of the line on a position versus time graph is equal to the velocity of the object. If the object is moving with a velocity of +4 m/southward, then the slope of the line will exist +4 m/s. If the object is moving with a velocity of -viii 1000/s, then the slope of the line will exist -8 m/south. If the object has a velocity of 0 m/s, then the slope of the line will be 0 yard/s. The gradient of the line on a position versus fourth dimension graph tells it all. Because of its importance, a student of physics must take a good understanding of how to calculate the slope of a line. In this part of the lesson, the method for determining the slope of a line on a position-time graph volition be discussed.

Allow's brainstorm by considering the position versus time graph below.

The line is sloping upwards to the right. But mathematically, by how much does it gradient upwards for every 1 second forth the horizontal (time) axis? To respond this question nosotros must utilize the gradient equation.

Using the Slope Equation

The slope equation says that the slope of a line is institute by determining the amount of rise of the line between any two points divided by the amount of run of the line between the same two points. In other words,

Pick two points on the line and determine their coordinates.
Determine the difference in y-coordinates of these two points (rise).
Decide the difference in x-coordinates for these two points (run).
Divide the deviation in y-coordinates by the difference in x-coordinates (rise/run or slope).

The diagram below shows this method being applied to determine the slope of the line. Note that three different calculations are performed for three different sets of two points on the line. In each case, the result is the aforementioned: the slope is x m/s.

So that was piece of cake - rise over run is all that is involved.

At present allow's try a more difficult case. Consider the graph below. Note that the slope is not positive but rather negative; that is, the line slopes in the downward direction. Note too that the line on the graph does non pass through the origin. Gradient calculations are relatively like shooting fish in a barrel when the line passes through the origin since one of the points is (0,0). Only that is not the example hither. Test your understanding of slope calculations past determining the slope of the line below. Then click the button to check your answer.

Check Your Understanding

1. Determine the velocity (i.e., slope) of the object as portrayed by the graph below. When you believe you know the answer (and non before), click the button to check information technology.