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Per second per second or (/s/s) refers to the rate of acceleration. If you are standing still and you increase your speed at a rate of 5 feet per second per second that means after 1 second you'll be moving at 5 feet per second, after two seconds you'll be moving at 10 feet per second, after three seconds you'll be moving at 15 feet per second, and so on. Every second that goes by, 5 more feet per second will be added to your speed. So 5ft/s/s is a rate of acceleration.

An easier example to understand, instead of per second per second, is per hour per second. If you are in a car that is standing still and you increase your speed at a rate of 5 miles per hour per second that means after 1 second you'll be traveling at 5 miles per hour. After 2 seconds your speed will have reached 10 mph. After 10 seconds you'll be traveling at 50mph. Each second that goes by you add 5mph to the speed.

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Q: What does per second per second mean?
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