Please wait for the animation to completely load.
When an object's velocity is changing, it is said to be accelerating. When an object speeds up, it's speed starts lower and increases, so that the average velocity will be different than it's speed at any one time. So how do we determine the instantaneous velocity? Play the first animation where the toy Lamborghini's velocity is changing (increasing) with time (position is given in centimeters and time is given in seconds). Restart.
Enter in a starting time of 0 s and and ending time of 10 s. 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 (0 s, 10 s). What is the Lamborghini's average velocity during the time interval (1 s, 9 s)? It is the slope of the new line segment shown when you enter in 1 s for the start and 9 s for the end and click the "show rise, run, and slope" button.
Please repeat this for the intervals (2 s, 8 s, 3 s to 7 s, 4 s to 6 s and 4.5 s to 5.5 s. : What do you notice about how the slope changes as you step the time interval inward towards 5 seconds? What do you think the speed of the car at the instant of 5s?
You can get a good-looking graph by right-clicking on the graph to clone the graph and resize it for a better view.
As the time interval gets smaller and smaller, the average velocity approaches the velocity at the instant of the midpoint as shown by the following Instantaneous Velocity Animation.
The instantaneous velocity therefore is the slope of the position vs. 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 Animation.