I think the question is self-explanatory but stackexchange requires me to write something here.
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$\begingroup$ I thought that it might be because it was close to $U$ and $V$ in the alphabetical order. It was just a speculation of mine, anyway. $\endgroup$ – Arch Stanton Mar 5 '18 at 16:00
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I’m pretty sure Lagrange started this, in Méchanique analitique (1788, p. 224; 1809, p. 263; 1811, p. 311; 1815, p. 2): his predecessors mostly worked with the vis viva ($=2T$) instead.
(As to why he chose the letter $T$, no idea. Words like kinetic, energy, work, appeared only later.)
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Gaspard-Gustave Coriolis and Jean-Victor Poncelet used the name "quantité de travail" (quantity of work) and "travail mécanique" (mechanical work) to denote the kinetic energy. I guess that this (the term "travail") could be the origin of the symbol $T$. See at the end of https://en.wikipedia.org/wiki/Vis_viva
(Be patient for my superficiality, I am very far from being a historian of science, I am just a mathematical physicist and this post migrated here from PSE.)
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$\begingroup$ Sorry it seems I took I mistake! I am correcting my answer. $\endgroup$ – Valter Moretti Mar 4 '18 at 8:57
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$\begingroup$ D. Bernoulli is mentioned in Wikipedia text, but not for using $T$. $\endgroup$ – Valter Moretti Mar 4 '18 at 9:05
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$\begingroup$ I forgive your mistake. I have to admit mathematical physics is an intriguing distraction. If you happen to be in Trieste, there's a beer and some company waiting :-) $\endgroup$ – Arch Stanton Mar 5 '18 at 1:47
