Main content

# Acceleration vs. time graphs

Learn how to interpret the motion of an object represented on an acceleration vs. time graph.

An acceleration vs. time graph represents the acceleration of an object at different times.

For example, if you read the y-value of the graph shown below at a particular time, you will get the acceleration of the object in meters per second squared for that instant.

**Try sliding the dot horizontally on the graph below to choose different times, and see how the acceleration changes.**

**Concept check:**According to the graph above, what is the acceleration at time

## What does the slope of an acceleration vs. time graph represent?

The slope of an acceleration graph represents a quantity called jerk.

**Jerk**is the rate of change of the acceleration.For an acceleration graph, the slope can be found from
$\text{slope}={\displaystyle \frac{\text{rise}}{\text{run}}}={\displaystyle \frac{{a}_{2}-{a}_{1}}{{t}_{2}-{t}_{1}}}={\displaystyle \frac{\mathrm{\Delta}a}{\mathrm{\Delta}t}}$ , as shown in the diagram below.

This slope, which represents the rate of change of acceleration, is the jerk value.

As strange as the name

*jerk*sounds, it fits well with what we would call jerky motion. If you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time, the motion would feel jerky, and you would have to keep applying different amounts of force from your muscles to stabilize your body.Finally, let's visualize the jerk with the example graph shown below.

**Try moving the dot horizontally to see what the slope—i.e., jerk—looks like at different points in time.**

**Concept check:**For the acceleration vs. time graph shown above, is the jerk positive, negative, or zero at