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Torricelli's Equation ($v^2=u^2+2as$) is usually presented as the particular formulation of the SUVAT system which doesn't involve t. It is derived from the others using some (perhaps well-motivated) algebraic tricks. Students are then advised to use it when they know three of $s,u,v$ and $a$, but not $t$.

Can anyone provide physical insight into this equation, how it is derived and in what situations is it useful.

pdmclean
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  • What on earth is the SUVAT system? What kind of question is "Why are the velocities squared" - the only possible answer is "Because the equation is correct that way". Also, Toricelli's equation has nothing to do with Torricelli's law, just as Euler's identity has nothing to do with the Euler characteristic. – ACuriousMind Mar 18 '15 at 02:07
  • @ACuriousMind: SUVAT is a term for kinematic equations ($s=vt+\frac12at^2$, etc). As it stands, this question is probably too broad to be reasonably answered here. – Kyle Kanos Mar 18 '15 at 02:25
  • Do you want me to break it up into a dozen questions? – pdmclean Mar 18 '15 at 02:28
  • Given that you mention DiffEq & IBP in the second half, I would have suspected the first half to have been rather trivial (especially since the Wikipedia pages you link give derivations). But yes, I think asking multiple questions (in multiple posts) is better than asking a boat load of questions in a single post. – Kyle Kanos Mar 18 '15 at 02:35
  • Suvat (also, Suvad) is a village in the Lachin Rayon of Azerbaijan. – yohBS Mar 18 '15 at 07:12
  • The letters 's', 'u', 'v', 'a', 't' are the ones that appear in the usual constant-acceleration kinematics equation in certain formulation. Not a formulation that I like because they rely on assigning a rigidly selected set of symbols to certain physical quantities (one of my pet peeve is students thinking that there is a magical connection between certain letters and certain physical quantities); both it is a moderately popular formulation. – dmckee --- ex-moderator kitten Mar 19 '15 at 00:41
  • I've narrowed the question - still it is quite open-ended. I have some more insight to add - in the direction of calculus – pdmclean Mar 19 '15 at 10:43
  • see http://physics.stackexchange.com/q/67432/ – pdmclean Mar 19 '15 at 11:18
  • How about rewriting it as $a=\frac{v-u}{x-x_0}\frac{v+u}{2}$ and interpreting $\frac{v-u}{x-x_0}$ as the slope of a chord of a trajectory in the $(x,v)$-plane and $\frac{v+u}{2}$ is the average of $v$. Here the curve is characteristed as having constant convexity $a$. – pdmclean Mar 19 '15 at 22:31
  • Crossposted from http://math.stackexchange.com/q/1194867/11127 – Qmechanic Mar 20 '15 at 21:06

1 Answers1

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It's just conservation of energy without being called as such.

$$\mbox{Energy}_{\mbox{before}}=\mbox{Energy}_{\mbox{after}}$$

$$\frac{1}{2}m v_1^2+m g h_1=\frac{1}{2}m v_2^2 +m g h_2$$

$$\frac{1}{2}m v_1^2=\frac{1}{2}m v_2^2 +m g (h_2-h_1)$$

$$v_1^2=v_2^2 +2g \Delta y$$

This seems trivial when you have calculus and a concept of energy, but without calculus it makes it seem like an important equation derived from the formula $y(t)=y_0+v_0t-\frac{1}{2}g t^2$.