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....

Extracting acceleration from a graph

The x - t and v - t graphs show the motion of a car starting from a stop sign. What is the car's acceleration?

Acceleration is defined as the slope of the v-t graph. The graph rises by 3 m/s during a time interval of 3 s, so the acceleration is (3 m/s)/(3 s) = 1 m/s2.

Incorrect solution #1: The final velocity is 3 m/s, and acceleration is velocity divided by time, so the acceleration is (3 m/s)/(10 s) = 0.3 m/s2.

The solution is incorrect because you can't find the slope of a graph from one point. This person was just using the point at the right end of the v-t graph to try to find the slope of the curve.

Incorrect solution #2: Velocity is distance divided by time so v = (4.5 m)/(3 s) = 1.5 m/s. Acceleration is velocity divided by time, so a = (1.5 m/s)/(3 s) = 0.5 m/s2.

The solution is incorrect because velocity is the slope of the tangent line. In a case like this where the velocity is changing, you can't just pick two points on the x-t graph and use them to find the velocity.

Last Update: 2009-06-21