 # Why is the speed of falling by gravity given as meters squared?

I would think that it would either be 1 dimentional, because it’s measuring along one axis, or 3 dimentional, because life is 3D. Anyone know the answer?

speed is always given as m/s, the gravity acceleration as m/s^2, I don’t understand your question, really.

paolo

Not quite sure what you mean but I’m guessing you are referring to acceleration due to gravity, i.e. g = 9.8 m/s^2.

It works just like any other acceleration. Maybe it’s easier to understand if you split it into (m/s)/s which means that every second the speed increases by 9.8 m/s

Don’t think of it as “meters per second squared” think of it as “meters per second per second” The “squared” is just because in math you can write (1/s)*(1/s) as (1/(s^2)). It’s nothing to do with the dimensions.

Now if I have a velocity, it’s meters per second. So 9.8 meters per second would be “it travels 9.8 meters in one second.” If it starts off next to you, one second later it’s 9.8 meters away.
Acceleration is change is velocity, so if we have an aceleration of 9.8 m/(s^2) and start it from stationary (eg drop something), then one second after dropping it, it’s travelling at 9.8 meters per second. Two seconds after dropping it it’s travelling at 19.8 meters per second and so on.

Oh, ok. I get it. Thanks.

It can be thought of as second order logic; but mathematically,the dimensions denote a constant with a dimension of variability. To show the variability in acceleration, it would be plotted as a curve; on a two dimensional plane. We think of there being 3 dimensions however there is also the dimension of time; which seems to have dimensions to it. There may even be more considering the rotation matrices associated with the Standard Model. That being said, dimensions in mathematics can have a metaphysical or metaphorical meaning.

…or do they? muahahaha

People mistake mathematical dimensions all the time. They are completely different to physical ones.

For example, a bicycle:

• It has position (3 dimensions)
• It has velocity (3 dimensions)
• It has angular position (3 dimensions)
• It has angular velocity (3 dimensions)
Even by this, you can see a 3-d object has 12 ‘dimensions’ or things that can be plotted onto an axis.
Then you could say:
• Height (one dimension)
• Mass (one dimension)
• Gears (one dimension)
• Current torque applied by feet (one dimension)
• Angle of handle bars

And before you know it you have a 17-dimensional bicycle! So what is a mathermatical dimension? Just something that can be plotted to allow comparison. Think of it like a parameter to a function, or an ingredient in a recipe. To determine the outcome you need to know all the inputs, or, all the dimensions.

Time? Is it a dimension? It’s a mathematical dimension, and a physical one, but not a spatial dimension. We know of only three spacial dimensions.

That depends upon what physics you’re speaking of. Classical Mechanics and Quantum Mechanics appear to tell differing and un-reconcilable stories. This is huge problem; as they must reconcile, whether or not we understand it. This is why I brought up the rotation matrices in the Standard Model. I also hinted at Einstein’s thoughts on time. :eek:

I’m not so sure that the math isn’t revealing an interesting truth. It doesn’t seem unreasonable to think that the instance of spacetime that we are aware of and interact with could be a module of a greater bulk. This isn’t something that I would argue adamantly of course; but on the same note, I couldn’t argue our epistemology on the reality of dimensions either. The evidence, though mathematical suggests lack of understanding that is corroborated with experimentation. :spin:

Though I have a great appreciation for Descarte’s word on the subject, I’m very skeptical as to whether it will be the last word. The order in the universe appears to occur at a frequency similar to that of chance. Statistical Mechanics may be the physics of the future; and not just thought of as a product of intellectual constraints. :o