Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

Velocity in the x-t graph

What is the velocity at the point shown with a dot on the graph?

q / Example: finding the velocity at the point indicated with the dot.
First we draw the tangent line through that point. To find the slope of the tangent line, we need to pick two points on it. Theoretically, the slope should come out the same regardless of which two points we picked, but in practical terms we'll be able to measure more accurately if we pick two points fairly far apart, such as the two white diamonds. To save work, we pick points that are directly above labeled points on the t axis, so that Δt = 4.0 s is easy to read off. One diamond lines up with x ≈ 17.5 m, the other with x ≈ 26.5 m, so Δx = 9.0 m. The velocity is Δx/Δt = 2.2 m/s.

Last Update: 2010-11-11