"Placement" isn't normally encountered in this sort of a problem. I suppose it might mean "starting somewhere". In the absence of other information, one might assume that one starts at the Origin.

Displacement is simply how far one has travelled.

Always, and the notation is ubiquitous, is this relationship for constant acceleration.

h_{0} is the place to start - your "placement", I suppose. If you start at zero, .

This leaves:

The first derivative: gives the velocity.

The second derivative: gives the acceletation.

It is this last equation that will fill your head with solutions.

Given v(t), find v'(t) to get the acceleration.

Given v(t), find the antiderivative to get the displacement. You will also need to know where to start.

Givenm then v(t) = t^2 - t, we have . In this case, since we are asked only how far things move, not where they land, we can ignore the initial displacement so that .

Simple enough, then, s(5) = (1/3)125 - (1/2)25 = 25((1/3)5 - (1/2))

That's enough of that. You tell me why Part B is even a different question. They look rather similar, don't they?

Hint: Is our friendly particla ALWAYS moving in the same direction?