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Velocity v's Time and Speed v's Time Graph

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3.10Velocity v's Time and Speed v's Time Graph


In these revision notes for Velocity v's Time and Speed v's Time Graph, we cover the following key points:

  • The properties of Velocity vs Time graph in the uniform motion
  • How to plot the corresponding Speed vs Time graph when the Velocity vs Time graph is given?
  • The meaning of the area under the velocity or speed vs time graph
  • The same for the uniformly acceleration (decelerated) motion
  • How to plot the Position vs Time graph when the corresponding Velocity vs Time graph is given?

Velocity v's Time and Speed v's Time Graph Revision Notes

Like in the Position vs Time graph, in the Velocity vs Time graph the horizontal axis contains the Time, t. Therefore, the velocity is shown at the vertical axis.

In uniform motion, the velocity is constant. This means the Velocity vs Time graph will be a horizontal line, which is equal to v units above or below zero depending on the sign of velocity. This line extends horizontally from zero up to the moving time t.

Since the speed cannot be negative (and time as well), the Speed vs Time graph will contain only the upper-right part of a two dimensional graph. Any negative part of the Velocity vs Time graph is flipped vertically and it will be considered as positive in the corresponding Speed vs Time graph.

If any section in the velocity vs time graph is in the negative part, the displacement (which is numerically represented by the area enclosed by the graph and the horizontal axis) is taken as negative.

There are two important properties regarding the relationship between the Velocity or Speed vs Time graph and the other kinematic quantities. They are:

  1. The area under (or above when negative) of the Velocity vs Time graph gives the Displacement, and
  2. The area under the Speed vs Time graph gives the Distance.

Velocity vs Time graph of a uniformly accelerated (decelerated) motion is a sloped straight line.

The speed vs time graph does not provide any information on the direction of motion. Therefore, the velocity vs time graph is more comprehensive than the corresponding speed vs time graph.

If we want to plot the Position (or Distance) vs Time graph for a motion with constant acceleration when the corresponding Velocity (or Speed) vs Time graph is given, we must consider a number of points (not only two as in the uniform motion) as the graph is a parabola. This is because more points taken, higher the accuracy of parabola plotting is.

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