I learned functions just purely as a mathematical concept, but I realised as I studied physics along with it, that it is actually a fundamental concept in the world. But I never really understood the phrase. For example, ‘velocity as a function of time’, yes I get that this would mean a v=tx form of graph, but what does it actually *mean*? Thank you
Edit: I made a mistake previously. I accidentally said ‘time as a function of velocity’
In: Mathematics
Functions simply describe relations between different quantities. Specifically, it’s something that you have a set of inputs for, it performs operations on them and then produces some output value. The phrase “Y as a function of X” simply states which quantities are outputs (*Y* here) and which are inputs (*X*).
“velocity as a function of time” would be something like *v*(*t*). Regardless of what the specific function looks like, it indicates that you’re interested in the velocity *v* and you know the time *t*. This can be relevant if you’re dropping something, or accelerating in a race.
It’s also possible to to have the inverse: “time as function of velocity”, *t*(*v*). In that case you’re saying that you know the velocity and are interested in the time. This can be relevant if you’re throwing something and want to know how long it takes for it to hit the ground again.
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