I am quite sure that your problem is how you think about physical quantities. That is, as soon as you read "force", you think of F, and equations that involves this F. So you associate each physical quantity, given in the problem, with the letter that represents it, and not with the actual meaning of that quantity. And the same goes with equations - you see them mostly as relationships between letters. So in your example, it goes like this:
Data given : m, v, d.
The problem asks for : F.
F is : F = ma.
We have the m, but not the a, so we don't know what to do now.
So, first of all, try to understand every physical quantity as good as possible, get the "feeling" of it. For example, the force is quite intuitively understood from our daily life - a big force pushes things hard, a small force hardly moves them at all. Try to get such feeling about every physical quantity. What's the difference between an object moving with acceleration and moving without it? What's the difference between an object having a huge momentum and a small one? This may sound trivial and stupid, but think again, what if I ask : What's the difference between a vector field with a high divergence and without it? (Don't mind that you probably don't even know what it is, it's just a more subtle question than the ones before). From my own experience I can tell, that only a small percentage of college students (at least in my university) could answer this in their own words, and not give the formal definition, that is, the plain letters, symbols.
The same goes with understanding equations, try to get the feeling of them. For example, F = ma. Let's write this in a more intuitive form : a = F/m. Why acceleration is proportional to force? Why acceleration is inversely proportional to mass? Easy, right? Then let's move forward : d = at^2/2 (d is distance traveled with constant acceleration a in time t, starting from zero velocity). Why the distance is proportional to the square of time, and not to time to the power of one or three? I would answer that like this : traveled distance in it's general form is d = average velocity * time. Average velocity in our example is (at)/2, since it goes from 0 to at continuously. So we get : d = average velocity * time = (at)/2 * t = at^2/2, as expected. So the distance is proportional to time squared because, first of all, as time passes, the average velocity raises (proportionally to t), and then we multiply this average velocity by time and get our t^2 proportionality. This is also quite easy, but what if the analysed equation is something like : something equals the volume integral of a sum of.. So you should constantly improve your ability to analyse physical quantities and relationships between them (equations). To say all of this in short : ask question "Why?" as frequently as possible to the textbook you read, to the teacher you listen to and to Life in general.
So let's return to the problem with the bullet.
To get the force, we still need the acceleration a, and we should somehow get it from the given distance d and velocity gained while traveling that distance v. Let's model this situation in our head : a bullet is traveling some distance d, while it is traveling it feels a force F, that gives it acceleration, and because of that the speed of the bullet rises constantly. It goes out of the distance d with v. Let's define t as the time that the bullet spent in the distance d. So the bullet was traveling with constant acceleration a in time t. What speed it gained in that time? v = at, right? But we don't know the time t, however, we know that the bullet's speed was rising continuously, from 0 to at = v, so the average speed was at/2 = v/2. So we know the distance, and we know the average speed, the time is simply t = d/v[avg] = 2d/v. Put this into v = at, we get : v = a * 2d/v => a = v^2/(2d), so the force F = ma = m * v^2/(2d).
Now, this could have been solved much faster using the energy conservation principle : the kinetic energy acquired by the bullet is mv^2/2, and the work done by the force to the bullet is F * d, both of them are equal, and we immediately get F = mv^2/(2d). So we didn't even need the formal definition F = ma.
So this is how it's done : you model the situation in your head, think about every quantity that is given, think about the relationships between them, and if you understood everything properly, the general idea how you could get the required quantity should come out.
. How do you decide what to wear? Whatever algorithm you use, it's a method that ensures you are dressed properly for the weather, activities, etc.
