The slope of an acceleration-time graph gives us:

The slope of an acceleration-time graph represents the rate of change of acceleration with respect to time, known as jerk. Jerk is the third derivative of position with respect to time and is measured in meters per second cubed (m/s³). 

It quantifies how quickly an object's acceleration is changing, which is particularly relevant in contexts where smooth motion is essential, such as in vehicle design to ensure passenger comfort.