The meter is a unit of distance. The second is a unit of time. Speed is the rate of change of distance. In a unit of time, your location changes by a unit of distance. After 1 second, your position is 1 meter from where it was a second ago, or some other distance, depending on your speed. If your speed is changing, you can also measure the rate of change of speed per unit time. In 1 second, your speed changes from 1 meter per second to 2 meters per second, so your acceleration is 1 meter per second (of speed) per second (of time elapsed).
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