mecànica clàssica

F = at


m·d_{tt}^{2}[x(t)] = at
d_{tt}^{2}[x(t)] = (a/m)·t


d_{t}[x(t)] = ( a/(2m) )·t^{2}


x(t) = ( a/(6m) )·t^{3}


E(t) = ∫ [ at ] d[x]
E(t) = ∫ [ at·d_{t}[x] ] d[t]
E(t) = ∫ [ at·( a/(2m) )·t^{2} ] d[t]


E(t) = ( a^{2}/(8m) )·t^{4}


(m/2)·d_{t}[x(t)]^{2} = ( a^{2}/(8m) )·t^{4}