We've already addressed the question of what speed and velocity are, but if you think carefully there is one problem remaining, and it is a somewhat subtle problem. We said an object's speed is the distance it travels divided by the time it takes to travel that distance, but what happens if the object changes speed during that time interval? If an object smoothly accelerates from 5m/s to 10m/s while you measure the distance it travels and the time it takes, what do you get? 5m/s? 10m/s 7.5m/s? The fact is the object's true speed is different at every point in time while we're measuring, that's what acceleration means. So to take into account this complication we need to differentiate between instantaneous and average speed. We do this in a very common sense sort of way. If we want to know the speed of the object right now, at this instant we should take our distance measurements at the beginning of "this instant", and the end of "this instant", but when we say "at this instant" we're really just talking about a really short period of time. A period of time so short that the speed doesn't have time to change. So that is it, the faster we make our time and distance measurements the closer we come to measuring the instantaneous speed. If we don't worry about taking the measurements quickly and just measure over any old time interval, then we're measuring the average speed on that time interval. The same is true for velocity, if you want the instantaneous velocity, then measure the velocity on a very short time interval. If you want the average velocity measure it on the time interval you want to average over.
If your read the answer to question 1. you know that the magnitude of the instantaneous velocity is the instantaneous speed. This warrants a little more discussion. First it is worth noting that when we say the words speed and velocity without the modifyer "average" we are talking about the instantaneous values. That being said it is also important note that it is the fact that we've chosen a time interval sufficiently short that the velocity doesnt' change on the time interval that causes the speed to be the magnitude of the velocity vector. The magnitude of the average velocity is not the average speed. This can be seen by looking at an object moving at constant speed in a circle averaged once around the circle. The average velocity is zero because the change in direction averages to zero, but the average speed is the same as the instantaneous speed because it is constant at all times.
© 2008 Kansas State University Physics Education Research Group.