What does a velocity-time graph represent?

The first step in answering any question is to figure out what the question really means! Velocity is a term physicists use to describe not just speed, but speed in a particular direction. When we talk about speed every day we mean the distance something moves in a particular time, but generally physicists prefer to talk about velocity - distance moved in a particular time in a particular direction - known as displacement. Then when we think about acceleration, we want to know how much the velocity is changing over time.

A velocity time graph is what we use to show how velocity changes with time. Time is drawn on the x-axis because it is the variable the scientist chooses to change (independent) and velocity is drawn on the y-axis because it is what the scientist measures (dependent).

Imagine watching a stationary car for 5 seconds. We see that the time goes by, but neither the direction or speed of the car changes. So if we plot a point at each second of the velocity of the car. We get a straight horizontal line from the origin to 5 seconds on the x-axis.

I would then go on to talk in the context of the car example how the line would change as the car picks up speed, slows down, and how this relates to acceleration. I would get them to do little experiments with a toy car to demonstrate these points.

I would then sum up how this relates to the key equations that arise from the graph including displacement.

I would then summarise the definitions and equations.