mecànica clàssica

F = at^{n}


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


d_{t}[x(t)] = ( a/((n+1)m) )·t^{n+1}


x(t) = ( a/((n+1)(n+2)m) )·t^{n+2}


E(t) = ∫ [ at^{n} ] d[x]
E(t) = ∫ [ at^{n}·d_{t}[x] ] d[t]
E(t) = ∫ [ at^{n}·( a/((n+1)m) )·t^{n+1} ] d[t]


E(t) = ( a^{2}/(2(n+1)^{2}m) )·t^{2(n+1)}


(m/2)·d_{t}[x(t)]^{2} = ( a^{2}/(2(n+1)^{2}m) )·t^{2(n+1)}