I can see no way to do part a). We need some reference point to determine the potential energy and we are not given one. So perhaps we could start with the definition that PE = 0 J at time 0. Then if we can calculate between time 0 and time T we could define the PE at time T to be equal to .

But wecan'tcalculate this! We know how much the kinetic energy has changed, but we know nothing about how the total energy has changed. (This tells us how much nonconservative work is being done.) For example, we could do the problem and come up with a specific answer if we knew the particle was moving across a flat plane (with friction or without friction?). But we come up with a different answer if the particle is flying through the air on a parabolic trajectory (with air resistance or without air resistance?) So the answers depend on the type of problem being done.

So either there is information about the problem you haven't given us or the question is worthless.

-Dan