Imagine instead of measuring speed in m/s, we measured it in terms of how fast a rabbit can hop. If you’re traveling at one rabbit, you’re moving at 15 meters per second. If I’m traveling at one rabbit now, and one second later I am traveling at two rabbit, it means my speed changed by one rabbit in that second, or one rabbit per second. Now we can just replace “rabbit” with “15 meters per second”, since they mean the same thing. I went from traveling at 15 meters per second to 30 meters per second, so I accelerated by 15 meters per second, per second.
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