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Questions tagged [calculus]

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Why is this equation correct?

This problem seems to be solved the exact same way in multiple solution books, so I'm certain that the way it is done is correct and that I'm just rusty when it comes to calculus due to multiple years ...
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How do you derive $v_f^2 = 2ad + v_i^2$ from $v_f = v_i + at$ and $d = v_it + (a/2)t^2$?

I'm trying to use substitution to find the equation Vf^2 = 2ad + Vi^2 from Vf = Vi + at and d = Vit + a/2(t^2), but I get stuck understanding part of the math. I've attached a picture, and you can see ...
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Can someone provide to me an intuitive explanation of the second integral of position with respect to time?

I am aware of what the first integral of position, absement means (at least to a very superficial level). However, I can find nothing regarding the physical intuitive meaning of absity, the second ...
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How would you calculate the half-life of a source with one long measurement?

I'm working on a project, and I understand that half life of a source is typically calculated with time intervals (eg 5 sec intervals for 20 minutes) and then using that data to find the decay ...
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