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Malhar Rajpal This is a follow-up article to one I wrote about deriving SUVAT (kinematic) equations - if you haven't read it yet, I suggest you check it out here. In this article, I will show you how to prove the last two SUVAT equations: Proof 1: s = ((v+u)/2) t This equation can be obtained by combining equations 1 and 2 (shown below) from the last article: We can rearrange the first equation to find a, giving a = (v - u)/t. We can then substitute this into the second equation, which gives the following: This brings us to the equation we wanted! There are also methods to derive this equation from scratch, but since we have already done the work to prove the first two equations, it makes sense to just use them. Proof 2: s = vt - 1/2 at^2 In my previous article, I proved both v = u + at and s = ut + 1/2 at^2. Rearranging v = u + at gives us u = v - at. We can now replace the u in s = ut + 1/2 at^2 with v - at to get the following: So we have proved that this equation is true as well!
I hope that you managed to figure out the proofs from the last article but if you didn’t, now you know! I find that it is always good practice to learn about how formulas are derived instead of blindly memorising them. That way, you can always be certain about what is true and what isn’t, and no one can trick you into believing a faulty formula. It is also helpful to remember what the formula is when you know where it comes from.
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