these numbers are values of the instantaneous speed the instantaneous speed is the speed of an object at a particular moment in time and if you include the direction with that speed you get the instantaneous velocity in other words eight meters per second to the right was the instantaneous velocity of this person at that particular moment in time note that this is different from the average velocity if your home was a thousand meters away from school and it took you a total of 200 seconds to get there your average velocity would be five meters per second which doesn't necessarily equal instantaneous velocities at particular points on your trip in other words let's say you jog 60 meters in a time of 15 seconds during this time you were speeding up and slowing down and changing your speed at every moment regardless of the speeding up or slowing down that took place during this path your average velocities still just gonna be four meters per second to the right or if you like, positive four meters per second say you wanted to know the instantaneous velocity at a particular point in time during this trip in that case, you'd wanna find a smaller displacement over a shorter time interval that centered at that point where you're trying to find the instantaneous velocity this it give you a better value for the instantaneous velocity but it still wouldn't be perfect in order to better zero in on the instantaneous velocity we could choose an even smaller displacement over that even shorter time interval but we're gonna run into a problem here because if you wanna find the perfect value for the instantaneous velocity you'd have to take in infinitesimally small displacement divided by an infinitesimally small time interval but that's basically zero divided by zero for a long time no one could make any sense at this in fact since defining motion at a particular point in time seemed impossible it made some anchient greeks question whether motion had any meaning at all they wondered whether motion was just an illusion eventually Sir Isaac Newton developed a whole new way to do math that let you figure out answers to these types of questions today we call the math that Newton invented calculus so if you were to ask a physicist what's the formula for the instantaneous velocity he or she would probably give you a formula that involves calculus but in case some of you have been taking calculus yet