Definition
The Italian physicist Galileo Galilei is credited with being the first to measure speed by considering the distance covered and the time it takes. Galileo defined speed as the distance covered per unit of time. In equation form, this is
where v is speed, d is distance, and t is time. A cyclist who covers 30 meters in a time of 2 seconds, for example, has a speed of 15 meters per second. Objects in motion often have variations in speed (a car might travel along a street at 50 km/h, slow to 0 km/h, and then reach 30 km/h).
In mathematical terms, the speed v is defined as the magnitude of the velocity v, that is, the derivative of the position r with respect to time:
If s is the length of the path traveled until time t, the speed equals the time derivative of s:
In the special case where the velocity is constant (that is, constant speed in a straight line), this can be simplified to v = s/t. The average speed over a finite time interval is the total distance traveled divided by the time duration.
Read more about this topic: Speed
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