Phy(KE)

Sure, they are also usable, W=KE=Q(heat chapter)=E.
May be you can analysis W=Fs from F=ma.
unit of W= kg m^2v^-22
unit of F= kg mv^-22
so W= F*S(length)

Both KE and W mean energy, however, KE is different in different condition,
KE can equal to 1/2mv^2+ mgh, so you need to take care when to use
1/2mv^2=Fs.

K.E. = (1/2)mv²
是當物體以速度(v)運行時，便知其動能為 K.E. = (1/2)mv²

如果 以 W=Fs 去計算，所付出的功為 W，但是否所有的功量 W 都全部變為動能呢？可能有問題吧！

物體置於光滑平面上受力加速！可以。
自由落體！可以。

但當物體置於非光滑平面上受力加速，有摩擦，有一部份功 W 會變為熱能，動能便不等於 FS 了。

Work done W = F.s where F is the applied force and s is the displacement of an object.

But F = ma (where m is the object mass, a is the acceleration)
and from the equation of motion: v^2 = u^2 + 2a.s
a = (v^2 - u^2)/2s
Therefore, W = m[ (v^2 - u^2)/2s].s = (1/2)m(v^2 - u^2) = (1/2)mv^2 - (1/2)mu^2
That is, the work done in bringing an object from rest (u = 0 m/s) to speed v
= (1/2)mv^2, which is termed as the kinetic energy possessed by the object

其實 Work Done = Fs 是假設了 F 是 constant。

正確的應用 integration

Work Done
= ∫ F ds = ∫ F v dt = ∫ mav dt = ∫ m dv/dt v dt = ∫ mv dv = (1/2) m v²

http://en.wikipedia.org/wiki/Kinetic_energy