Here's why:

* Acceleration is the rate of change of velocity. This means it tells us how quickly the velocity is increasing or decreasing.

* Velocity vs. Time Graph: This graph plots velocity on the vertical axis and time on the horizontal axis.

* Slope: The slope of a line on a graph represents the change in the vertical axis divided by the change in the horizontal axis.

In the context of a velocity vs. time graph:

* The change in the vertical axis represents the change in velocity.

* The change in the horizontal axis represents the change in time.

Therefore, the slope of a velocity vs. time graph is:

(Change in Velocity) / (Change in Time)

This is precisely the definition of acceleration.

Example:

Imagine a car moving at a constant velocity of 10 m/s. On a velocity vs. time graph, this would be a horizontal line. The slope of this line is zero, indicating zero acceleration (the car is not speeding up or slowing down).

If the car then accelerates to 20 m/s over a period of 5 seconds, the line on the graph would slope upwards. The slope of this line would be (20 m/s - 10 m/s) / (5 s) = 2 m/s², which is the acceleration of the car.