Originally posted by CaptBevvil:
What... but... that's not why the equation has a velocity squared term in it."The formula is KE = ½mv². It indicates that the energy of motion is in proportion to mass times velocity squared. Squaring the velocity is the problem, because no mass can move at velocity squared. As a result, the formula is an abstraction apart from the motion of the mass.
Okay. Technically the application of work on a mass results in a change in energy. Therefore,
W = E[sub]kf[/sub] - E[sub]ki[/sub].
Given that Work is also equal to Force multiplied by the distance over which that force is applied (since the two have a linear relationship),
W = Fd,
and given Newton's second law, F= ma:
W = mad.
E[sub]kf[/sub] - E[sub]ki[/sub] = mad.
Given that,
a = Δv / Δt
a = (v[sub]f[/sub] - v[sub]i[/sub]) / Δt
aΔt = v[sub]f[/sub] - v[sub]i[/sub].
v[sub]f[/sub] = v[sub]i[/sub] + aΔt
and given that,
mean = (sum of elements) / (number of elements)
mean velocity = d / t
d / t = (1/2)(v[sub]f[/sub] + v[sub]i[/sub])
d = (1/2)(v[sub]f[/sub] + v[sub]i[/sub])t
d = (1/2)(v[sub]i[/sub] + v[sub]i[/sub] + at)t
d = (1/2)(2v[sub]i[/sub] + at)t
d = v[sub]i[/sub]t + (1/2)at^2
E[sub]kf[/sub] - E[sub]ki[/sub] = m * a * (v[sub]i[/sub]t + (1/2)at^2)
Assuming the object starts at rest,
E[sub]kf[/sub] = (1/2) * m * a^2 * t^2 = (1/2) * m * (at)^2
Given (see above)
at = v[sub]f[/sub] - v[sub]i[/sub]
and given that the object started at rest,
at = v[sub]f[/sub]
E[sub]kf[/sub] = (1/2) * m * v^2
E[sub]k[/sub] = (1/2)mv^2
Therefore, your degree came from a diploma mill. Q.E.D.