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
Metres measure distance.
Metres per second measure speed. (How much your position changed in one second)
Metres per second per second measure acceleration. (How much your speed changed in one second)
And you could go on… metres per second per second per second measures rate of acceleration increase (how much your acceleration changed in one second)
It’s the unit of acceleration.
It’s the rate of change of the velocity.
Push something, like a ball, down a hill, and you’ll notice it’s travelling the quickest towards the bottom of the hill.
When you’re driving and you put the gas pedal down, and you pull away from the car behind you.
Imagine you’re a spherical cow in outer space. You want to start moving towards some tasty gas grass. You can’t just teleport there, you have to move there. So you start moving. How fast are you moving? You are going 10 meters every second. That is meters per second, or m/s. This is velocity. But wait, you didn’t suddenly and instantaneously start moving that fast, you had to get up to that speed. It turns out, every second you were going 1 meter per second faster than the previous. You are increasing your speed at one meter per second per second or 1 m/s^2. This is acceleration. It’s how fast you are changing your velocity, measured in distance over time, over time. It’s a rate of change of a rate of change.
Note: speed is direction less, velocity is a vector, it has a direction. Hence my use of speed and velocity in those specific circumstances.
Also note: this is calculus. Calculus is all about rates of change. If you take the derivative of something, that’s a rate of change. Velocity is the derivative of position, and acceleration is the derivative of velocity. This is why it’s position over time, and then that previous quantity over time again. You can use this to derive almost all of Newtonian physics in fact.
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.
Meters per second is speed. If you move for one second at one meter per second, you travel ome meter. If you move for one second at two meters per second, you travel two meters. A meter is 39.37 inches.
Miles per hour is speed also. If you walk at three miles per hour for one hour, you travel three miles.
Speed is Velocity.
Acceleration is when something travels at a faster velocity for each second. A rock falling from an airplane speeds up as it falls. A penny dropped one foot over your head is nothing. From the top of a skyscraper, it would hit much harder.
You know when people talk about how fast a car can accelerate they say stuff like:
> “Zero-to-sixty (mph) in 4.72 seconds!” (in America)
> “Zero-to-one-hundred (km/h) in 4.88 seconds!” (in not-America)
This means that the car can go from a speed of 0.0 mph and get up to 60.0 mph in 4.72 seconds. On average, this means that the car increases speed by (60.0mph)/(4.72s)=12.7mph/s which makes sense: after 1s you’re up to 12.7mph, by 2s you’re up to 25.4mph, by 3s to 38.1mph, 4s to 50.8, and 5s to 63.5… which means we must have “hit 60mph” around that last quarter of a second (so it looks like our math did work out correctly).
But, mph is a derived unit of “miles per hour” which means that 1mph=1mi/h and so we could also write our math above out as 12.7mph/s=(12.7mi/h)/s… which, if we deal with all the numerators and denominators correctly, means that (12.7mph)/s=(12.7mi)/(h * s) or 12.7 miles per hour-second. Now, that might sound like a weird way to write things out, but in a lot of complicated mathy situations it is a nicer to have just one numerator and one denominator rather than having a bunch of nested fractions to keep track of.
Meters per second squared is the exact same kind of thing, except instead of measuring speed in mi/h it is measured in m/s. That means, because 12.7mph=5.68m/s that our (1.27mi/h)/s calculation is equivalent to (5.68m/s)/s and the car is accelerating by 5.68 meters-per-second every second – or if we do the simplified-fractions math – the car accelerates 5.68 meters per second-second. (Or, in other words “5.68 meters per second-squared.”)
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).
The fundamental subject is dimensional analysis, and you kind of have to understand derivatives and integrals to fully get it. But the ELI5 key is to understand some measurements are dimensions and others are derivatives, which means they are derived from the dimensions. The most common dimensions are space and time. ‘x, y, and z’ Cartesian coordinates are spacial and refer analogously to oneself as forward/back, left/right, and up/down. Time generally moves in one direction, forward.
So, the base measurement is time, ever second a second passes. Simple enough.
The first derivative/derived measurement, is velocity. If one second passes and you move 1 meter in a particular direction, then another second passes, and you move another meter in the same direction. You are moving 1 meter every second, 1m/s,
The second derivative/derived measurement, is acceleration. If one second passes and you move 1 meter in a particular direction, then another second passes, and you move another 2 meters in the same direction, then a third where you move 3 additional meters, etc. You are not moving at a constant velocity, but are accelerating at a constant rate. Every second that passes, your velocity is increasing by 1 meter per second, thus one meter per second, . . . per second.
Absent relativistic effects, time is constant, but at any moment in time your position, your rate of movement [velocity], and your rate of acceleration can change, That goes back to the key mentioned above, derived measurements are measurements of change relative to constants like space and time. Under the concepts of time, position, speed and acceleration, their relative relationship is always the same, because they are defined relative to each other. And the expression of the changing values is expressed in terms of that relationship. No matter the measurement system, position will be a coordinate [ie, x,y,z], velocity will be a change in position over a period of time [change in distance over change in time dx/dt], and acceleration will be a change in velocity over a period of time [change in distance over change in time over change in time d^2x/dt^2].
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