# What does the velocity equation prove?

1. Oct 24, 2014

### avito009

Does this equation $$v^2= \frac {2E_k} {m}$$ prove that the velocity is inversely proportional to the mass of the object?

2. Oct 24, 2014

### Matterwave

That equation doesn't "prove" anything. Equations don't "prove" things, they just give you relations between things. That equation gives you the relationship between the velocity, the kinetic energy, and the mass. Usually the equation is written like so: $$E_k=\frac{1}{2}mv^2$$ to emphasize that this equation tells you what the kinetic energy is, given the velocity. The higher the velocity, the higher the kinetic energy. A statement like "velocity is inversely proportional to the mass of the an object" is not a useful statement. At the very least you would have to specify that "given the kinetic energy is constant, the velocity is inversely proportional to the square-root of the mass". Although true, that statement is too convoluted to give much physical insight. A much more useful statement would be "the kinetic energy of an object is proportional to the object's mass and to its velocity squared."

3. Oct 24, 2014

### ShayanJ

Well, I can have $v=-gt+v_0 \Rightarrow t=\frac{v_0-v}{g}$. Does it mean that Newtonian mechanics predicts how a freely falling object experiences time, depends on the acceleration of gravity of that place and its initial velocity???