What am I doing wrong here?

math belongs on reddit go away

>>8591160
>/sci/ - Science & Math
>math belongs on reddit go away

>>8591155
[math]
F = m\frac{dv}{dt} \\
Ft = mv \\
\int Ftdv = \int mvdv \\
E_k = \int Ftdv = \frac{1}{2} mv^2
[/math]

>>8591167
That's what i did initially, but that doesn't show me how pic is incorrect.

>>8591171
Because you can't just naively multiply the two velocities together. They're time averaged at that point.

>>8591155
Error was right at the begining. Acceleration isn't just v/t. Its Delta v/ Delta t. Relatively easy fix gives you the factor of a half your missing if you want to go in the spirit of you linear approximation, use constant acceleration and work backwards. Constant velocity gives a trivial result

>>8591173
Bzzzzt not relevant

>>8591178
Yeah, it actually is. Don't be a dumbass and think you know better than everyone else.

>>8591173
>>8591177
These two help you get to the answer you are looking for OP.

When writing v = d/t, you are assuming that the velocity is constant, which would mean that the acceleration is null.
But then, you write a = v/t which implies that the acceleration is constant and that the velocity is linearly growing, which is in contradiction with your first hypothesis, hence the contradiction in your conclusion.

>>8591155
Do you know how simple differentiation works? Christ.

>>8591424
I was doing differentiation, then found at line 3 I get different results if I integrate both sides compared to multiplying both by velocity. I could have treated line 2 as a separable DE, but i'd get the same result ignoring the constant

>>8591438
>>8591438
I think second last line you need to integrate, not differentiate. Then your kinetic energy should be correct, 1/2(mv^2)