When energy is not conserved: time and velocity-dependent potentials?

[sajid_mcse]

My Teacher question is
if the potential depends explicity on time t and/or on velocity v then energy of particle is not conserverd. Explain and prove.

 

[dextercioby]

What are your ideas on this topic ?

 

[nadeemo]

hmm I am not too sure how right this is but

any force crossed with the del operator equals 0 if a force is conservative

which means it depends on position explicitly?
...hope that helps somehow