Please wait for the animation to completely load.
When an object's velocity is changing, it is said to be accelerating. In this case, the average velocity over a time interval is (in general) not equal to the instantaneous velocity at each instant in that time interval. So how do we determine the instantaneous velocity? Restart. Play the first animation where the Lamborghini's velocity is changing (increasing) with time (position is given in meters and time is given in seconds).
Click the Show Rise, Run, and Slope button. The slope of the blue line segment represents the Lamborghini's average velocity, vavg, during the time interval [5 s, 10 s]. What is the Lamborghini's average velocity during the time interval [6 s, 9 s]? It is the slope of the new line segment shown when you enter in 6 seconds for the start and 9 seconds for the end, and click the Show Rise, Run and Slope button.
When you get a good looking graph, right-click on it to clone the graph and resize it for a better view.
What is the Lamborghini's average velocity, vavg, during the time interval [7 s, 8 s]? How about the average velocity during the time interval [7.4 s, 7.6 s]? As the time interval gets smaller and smaller, the average velocity approaches the instantaneous velocity as shown by the second animation.
The instantaneous velocity therefore is the slope of of the position versus time graph at any time. If you have taken calculus, you know that this slope is also the derivative of the function shown, here x(t). The Lamborghini moves according to the function: x(t) = 1.0*t2, and therefore v(t) = 2*t which is the slope depicted in the Instantaneous Velocity Simulation.