How To Find Velocity On A Graph

It was learned earlier in Lesson iv that the gradient of the line on a velocity versus fourth dimension graph is equal to the acceleration of the object. If the object is moving with an dispatch of +4 yard/s/s (i.due east., changing its velocity past four m/due south per second), then the slope of the line will be +4 1000/s/s. If the object is moving with an acceleration of -8 thou/southward/s, then the gradient of the line will be -8 m/s/s. If the object has a velocity of 0 m/s, then the slope of the line will be 0 m/s. Because of its importance, a pupil of physics must have a skillful 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 velocity-time graph will be discussed.

Let'due south begin by considering the velocity versus fourth dimension graph beneath.

The line is sloping upwards to the right. Just mathematically, past how much does it slope upwards for every 1 second along the horizontal (fourth dimension) axis? To answer this question we must use the slope equation.

Using the Slope Equation

The slope equation says that the slope of a line is plant by determining the amount of rising of the line betwixt whatever two points divided past the corporeality of run of the line between the aforementioned two points. A method for conveying out the calculation is

Option two points on the line and determine their coordinates.
Decide the difference in y-coordinates for these two points (rising).
Determine the divergence in ten-coordinates for these 2 points (run).
Divide the departure in y-coordinates by the difference in ten-coordinates (rise/run or slope).

The calculations beneath shows how this method can be applied to make up one's mind the slope of the line. Annotation that three unlike calculations are performed for 3 unlike sets of ii points on the line. In each case, the upshot is the same: the slope is 10 one thousand/s/s.

For points (5 s, 50 thousand/s) and (0 southward, 0 thousand/s):

Slope = (50 thou/south - 0 m/southward) / (5 due south - 0 southward) = 10 one thousand/s/due south

For points (5 due south, l m/s) and (2 s, 20 chiliad/south):

Slope = (fifty m/s - 20 m/due south) / (5 s - ii s) = 10 one thousand/s/due south

For points (4 s, twoscore thousand/s) and (3 due south, 30 m/s):

Gradient = (xl m/s - thirty yard/south) / (4 due south - 3 southward) = 10 g/southward/s

Observe that regardless of which 2 points on the line are chosen for the slope calculation, the event remains the same - ten m/s/s.

Cheque Your Understanding

Consider the velocity-time graph below. Determine the acceleration (i.due east., slope) of the object equally portrayed past the graph. Use the button to view the answer.

We Would Similar to Propose ...

Sometimes it isn't plenty to just read about it. You accept to collaborate with it! And that'south exactly what you do when you employ i of The Physics Classroom's Interactives. We would like to suggest that you combine the reading of this folio with the use of our Two Stage Rocket Interactive. This Interactive is institute in the Physics Interactives department of our website and allows a learner to apply the skill of computing slopes and relating them to acceleration values for a 2-stage rocket.