I googled this but I still don’t get it. I’m not mathematics inclined at all so literally make this a ELI5!
In: 11
Its a measure of acceleration!
Metres per second is speed – the amount of distance (measured in metres) that an object gain per second.
Metres per second per second is the amount of *speed* that an object gains per second.
If each second, an object is moving 1 m/s faster than it was the second before, it’s acceleration is 1 m/s *per second*
This is a unit of acceleration
One second ago I was moving at 1m/s
Now I’m moving at 2m/s
So I accelerated at 1m/s *per second*, or 1m/s^2
Velocity is the change in how far you go over time. Meters per second means “how far you have gone, in meters, each second.”
Acceleration is the change in velocity. Meters per second *per second* means “how much your speed, in meters per second, changes each second.”
So if you start at a velocity of 10 meters per second, and your acceleration is 10 meters per second per second, then after one second you will be going at 20 meters per second. After two seconds you will be going at 30 meters per second.
It is a measure of acceleration as opposed to a measure of velocity. So velocity or speed is how far something is travelling in a second, acceleration is how fast the velocity is changing, so the more seconds go past there is an increase in how fast something travels in a second. So if you jump from an aeroplane initially you aren’t going very fast, but as you continue to fall you accelerate, so by the time you hit the ground you are going fast enough to kill you.
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.
It’s a unit of acceleration, i.e. how quickly you are *changing* velocity. You can measure velocity itself in meters per second (or, say, miles per hour) which in turn is how quickly you are gaining distance.
Consider the mph example. A vehicle traveling at a velocity of 50 mph will cover 50 miles in 1 hour, of course. But to get to that 50 mph velocity, let’s say it started from a 0 mph standstill and took 5 seconds to reach 50 mph. Its change in speed (50 mph) divided by the time it took (5 s) gives it an acceleration of 10 mph/s. Then, when it reaches 50 mph, its acceleration drops to 0 mph/s again as it continues to cruise at constant velocity.
Meters per second (M/s) is velocity – how fast something is moving.
Meters per second per second (M/s^2 ) is acceleration – how fast something is changing it’s current speed.
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Tim and Eric start running across the playground. Over 5 seconds, they both move 10 meters. That’s a speed of 10 meters per 5 seconds, or 2 meters per second.
Tim says, “for every second we run, I’m going to go one meter per second faster!”
Eric says, “don’t do it Tim, your hubris will be your downfall!”
By 6 seconds, Eric has run 12 meters, still at 2 m/s. Tim has run 12.5 meters, now at 3m/s.
Tim says, “You can’t possibly imagine my conviction, Eric!”.
By 10 seconds, Eric has run 20 meters, still at 2 m/s. Tim has run 32.5 meters, now at 7m/s.
Eric says, “Tim, your mortal form can’t sustain this!”
By 30 seconds, Eric has run 60 meters, still at 2 m/s. Tim has run 372.5 meters, now at 27 m/s.
Tim says, “Your laws can only contain those who listen to them, Eric.”
By 60 seconds, Eric has run 120 meters, still at 2m/s. Tim has run 1632.5 meters, now at 57 m/s.
Eric says, “TIM! PLEASE I BEG YOU, DON’T DO THIS!”. Tim cannot hear him.
By 120 seconds, Eric has run 240 meters, still at 2m/s. Tim has run 6852.5 meters, now at 177 m/s.
Tim says, “Look at me Eric, witness my triumph!”
By 240 seconds, Eric has run 480 meters and stops. Tim has run 28092.5 meters, now at 237 m/s.
Eric tries to catch his breath, “Tim…don’t…”. Eric’s words are useless. Tim is soon faster than sound.
By 10 minutes, Eric begins to weep. Tim has run 178212.5 meters, now at 602 m/s.
Tim says, “I don’t need Eric, I don’t need anyone.”
By 20 minutes, Tim has run 716412.5 meters, now at 1202 m/s, faster than any any aircraft has flown.
Tim says, “I cast off my mortal bindings, I am unending.” His own ears can’t hear his words.
By 30 minutes, Tim has run 1,614,612.5 meters, now at 1802 m/s.
Eric weeps.
By 60 minutes, Tim has run 6,469,212.5 meters, now at 3602 m/s.
Tim says, “My eyes cannot make sense of the passing images, and yet, something is there.”
By 2 hours, Tim has run 51,782, 425 meters, now at 7202 m/s. He passes Eric, weeping in the playground, as he circumnavigates the Earth.
Eric’s eardrums explode as Tim passes.
By 5 hours, Tim has run 161,946,012.5 meters, now at 18002 m/s, faster than any manned spacecraft.
Tim says, “Eric, I think I perceive something, out there, waiting. I wish you could have been stronger Eric.”
By 10 hours, local search and rescue is fanning out from the playground, hoping to find Tim. No one believes Eric’s cries. “We started racing across the playground, and he started going at 1 meter per second per second, speeding up.” The police shake their heads. “We need a vector, not just acceleration. Please Eric, tell us the truth.” Eric cannot hear him, because his ear drums were destroyed 8 hours ago.
Tim has run 647,892,012.5 meters, and his body is now nothing but energy.
“It’s beautiful Eric. I understand now, I understand everything.” Tim says.
A thing is going 5 m/s. That’s a speed of 5 meters per second
A second later, its speed is now 10 m/s.
After another second, its speed is 15 m/s.
After another second, its speed is 20 m/s.
So it looks like for every second of time, the speed goes up by 5 m/s, right? That means the thing is accelerating, with an acceleration of 5 m/s per second. Aka the speed is changing by 5 meters per second, per second.
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