Maybe I just am having a hard time seeing which equation to use when - for example:
"A particle moving at 5 m/s reverses its direction in 1 s to move at 5 m/s in the opposite direction. If its acceleration is constant, what distance does it travel?"
Here I am thrown off completely because I know if I use one of the kinetics eqs, I get displacement, which is not what they are asking for in this situation. How would I find distance here?
Well, if they're asking for "distance" instead of "displacement", I would split the problem up into two parts: when the particle is moving in one direction (the initial direction, let's call it the + direction), and when the problem is moving in the opposite direction (the - direction).
So, by the wording of the problem, it's a bit ambiguous as to whether "1 second" refers to the time it takes for the particle to go from 5 m/s to -5 m/s OR the time it takes for the particle to simply "reverse direction", i.e. go from 5 m/s to 0 m/s.
Assuming it's the latter, it's easy. We'd just set it up:
vi = 5 m/s, vf = 0 m/s. (This is because the acceleration is in the opposite direction of its initial velocity, so at some point, the particle is going to stop and start to reverse directions.) So, we get:
vf = vi + at
0 = 5 + a(1)
a = -5 m/(s^2)
Plugging into:
vf^2 = vi^2 + 2ax
0^2 = 5^2 + 2(-5)x
x = (-25)/(-10) = 5/2 = 2.5 m
So now, we need to find the distance it travels starting from here at vi = 0, to vf = -5 m/s. An important thing to understand here is that it takes the same amount of time to move from vi = 5 m/s to vf = 0 m/s, as it does from vi = 0 m/s to vf = -5 m/s, when the particle is under the same constant acceleration.
An example of this is, let's say you're on a cliff, and you throw a ball up with a certain vi, let's say vi = 5 m/s (up is +). When the ball comes back down to the same height (i.e. height of the cliff), its velocity will have the same magnitude as the initial velocity, but the opposite direction, i.e. vf = -5 m/s (pointing down). (Here the constant acceleration is of course due to gravity.) You can prove this to yourself using the kinematics equations. But after that, just remember that fact... it comes in handy.
Therefore, the total distance the particle has traveled is 2 x 2.5 m = 5.0 m. The total displacement, on the other hand, is 0 m. Think of the cliff problem. If it's not so clear, I'll try to explain the cliff thing better.
