Proof of kinetic energy
work done equals a change in kinetic energy in a mechanical system.
δW = F.ds
W = ∫F.ds
W = m∫a.ds
W = m∫(dv/dt).ds
W = m∫v.dv
here if v and dv are in the same direction the change in kinetic energy will be the usual equation. what happens if both are in different...