When you’re talking meters per second per second, you’re talking about acceleration. Acceleration is the rate at which your velocity is changing. Velocity is expressed as distance per unit time… in your example, meters per second. If you’re talking about much your velocity is changing, you introduce another time element to express that rate. Say, for example, your velocity increases by 5 meters per second every second. Then you are accelerating (your velocity is changing) at a rate of 5 meters per second per second. It just means that every second, your velocity is five meters per second faster than it was a second ago. At time 0: 0 meters/second –> At time 1 second: 5 meters/second –> At time 2 seconds: 10 meters/second.
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