No, this is not homework ;-) I'm afraid it was some time ago I had one. I'm just studying on my own to cover any "holes", and I have apparently found the first one.

The problem is on motion, and under an optional section "kinematics equations derived from calculus": Given an initial velocity, and acceleration as a function of the velocity, calculate the time of a specific velocity. Or to be specific, when the velocity is half of the initial.

v= 1.50 m/s_{i}

a= -3.00v^{2}

That is, I think, I must find an equation relating the velocity and time. This is my feeble attempt:

a = dv / dt

dv = a dt

v= Sa dt+v("S" is supposed to be an integral sign)_{i}

So far this feels right, since the final velocity should be the initial plus the sum of all changes of the velocity (ie. the acceleration), although it also feels very suspicious. But continuing...

v= S (-3.00v^{2})dt+v_{i}

v= -3.00v^{2}t+v_{i}

...which is non-sense. However, blindly solving fortand puttingv=v/ 2, gives an answer exactly twice of the correct answer._{i}

Ok, I'm stuck here, and very ticked off that I cannot work it out even though it should be a simple and common calculation. I would be *very* greatful if someone, besides showing the right way to solve this, could make a guess at why I can't solve it. That is, what "hole" I need to fill in.

EDIT: I just realized that this might not belong in the "General Science" forum, sorry...