A graph that shows velocity plotted against time for a particle moving in a straight line. Let x(t) and v(t) be the displacement and velocity, respectively, of the particle at time t. The velocity–time graph is the graph y=v(t), where the t-axis is horizontal and the y-axis is vertical with the positive direction upwards. When the graph is above the horizontal axis, the particle is moving in the positive direction, when it is below the horizontal axis, the particle is moving in the negative direction.
The gradient of the velocity–time graph at any point is equal to the acceleration of the particle at that time. Also,So, with the convention that any area below the horizontal axis is negative, the area under the graph gives the change in position during the time interval concerned. Note that this is not necessarily the distance travelled.
(Here a common convention has been followed in which the unit vector i in the positive direction along the line has been suppressed. The displacement, velocity and acceleration of the particle are in fact vector quantities equal to x(t)i, v(t)i and a(t)i, where v(t)=ẋ(t) and a(t)=v̇(t).)