What does a velocity-time graph tell you?

On a velocity-time graph, the horizontal axis (x-axis) represents time, usually in seconds ($s$). The vertical axis (y-axis) represents velocity, usually in meters per second ($m/s$). If you pick any point on the line, the y-value tells you the object's exact velocity at that specific time. A positive velocity means the object is moving forward, while a negative velocity (below the x-axis) means it is moving backward.

The steepness, or slope, of the line tells you the object's acceleration. Acceleration is the rate at which velocity changes. Mathematically, the slope is the change in velocity divided by the change in time, or $a = \frac{\Delta v}{\Delta t}$. A steep upward slope means the object is speeding up rapidly. A gentle downward slope means it is slowly hitting the brakes. If the line is perfectly flat and horizontal, the slope is zero, meaning the velocity is constant and the object is not accelerating at all.

The most powerful trick of a velocity-time graph is that the area between the line and the x-axis represents the object's displacement, or change in position ($\Delta x$). Because area is generally length times width, multiplying a time ($s$) by a velocity ($m/s$) gives you a distance in meters. For a straight, flat line, you just calculate the area of a rectangle. If the velocity is changing, you might need to calculate the area of a triangle ($Area = \frac{1}{2} \cdot base \cdot height$).

The most common mistake is reading a velocity-time graph as if it were a position-time graph. On a position-time graph, a flat line means the object is standing still. But on a velocity-time graph, a flat line means the object is still moving, just at a steady speed. Always check the labels on the y-axis before you start answering questions!