Finding uniform transmission condition

[vin300]

We have never discussed about constant mechanical power transfer for the linear case, as against rotational well documented gear transmission. The energy acquired by linear motion, if varies linearly, then 0.5mv^2 must have constant differential. Trying it, if u=0, v=at.
d/dt[0.5m(at)^2]=constant. m(a^2)t=const.Hence concluding, a is inversely proportional to root of time, and the force to be applied is proportional to {sqrrt.(m/t)}. Does this look fine?

 

[BvU]

Who is "we"?

"The energy acquired by linear motion, if varies linearly, then 0.5mv^2 must have constant differential "
My interpretation: if you apply a constant power for linear acceleration, then the kinetic energy increases linearly with time.

v = at doesn't fly, though: that's only for constant acceleration. Here if ${1\over 2} mv^2 = B\, t$ with $B$ constant.
However, $a$ is still $\propto \sqrt{1/t}$, but not $\propto \sqrt{m}$.

Do check my claims, please !

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