Seeing that there has been quite a few people doing Motion in Unit 2 now. Most of the questions asked have been pretty much the same and most of my answers have also been pretty similar. I tried to avoid giving away the answer completely and instead try to give some direction on how to approach these questions. I thought I'd write up this general guide of how I approach these motion questions. I guess it does kind of apply to Unit 3 Motion as well. Hopefully it will help people understand that these motion problems are really quite a breeze, it's really just figuring out what's going on in the question and then applying the correct formula. You can apply this approach to most of the questions you'll come across in VCE Physics.
Motion questions are best approached methodically. I once read that Richard Feynman outlined his thought process as something like:
1. Write down the problem
2. Think real hard about it
3. Write down the solution
Okay, well maybe that's not helpful, but it's still funny. This list provides a more detailed method, but may seem kind of pedantic. It's still good to refer back to when you get stuck.
Read the problem carefully twice.
Reduce the problem to its essentials.
Draw and label a suitable diagram.
List the given quantities and the required quantities.
Put down some relevant principles (usually in mathematical form).
Analyze the problem, think about it, correlate the various factors, grind out some useful ideas. [9]
Solve algebraically as much of the problem as possible (very important, especially in complex problems).
Complete the numerical solution. (Do not do lengthy arithmetic ‘longhand’; use a slide rule.)
Check the problem.
Check the units.
Look critically at the answer. Does it seem like a reasonable answer? Develop your technical judgment by making a decision. [10]
Look up the answer in the answer book.
If your answer is correct, review the problem; otherwise correct the problem and then review it. In either case, be sure to review it.
I don't have a copy of the year 11 textbook anymore, so I'll just be using an example from:
MIT Kinematics Practice PaperThe high school section of MIT OpenCourse Ware has a lot of interesting problems and material for physics.
So here's the question:
During a track event two runners, Bob, and Jim, round the last turn and head into the final stretch with Bob a distance 
in front of Jim. They are both running with the same velocity 
. When the finish line is a distance 
away from Jim, Jim accelerates at a constant 
until he catches up to Bob and passes him. Jim then continues at a constant speed until he reaches the finish line.
a) How long did it take Jim to catch Bob?
b) How far did Jim still have to run when he just caught up to Bob?
c) How long did Jim take to reach the finish line after he just caught up to Bob? Bob starts to accelerate at a constant 
at the exact moment that Jim catches up to him, and accelerates all the way to the finish line and crosses the line exactly when Jim does. Assume Bob’s acceleration is constant.
d) What is Bob’s acceleration?
e) What is Bob’s velocity at the finish line? Who is running faster?
As you can see, this is probably harder than most questions that you'll come across with Motion in VCE Physics. But you can also probably see that it's quite similar to the type of questions you would have already encountered.
So yeah, first step is to distill all the information you can get out of the problem statement.
During a track event two runners, Bob, and Jim, round the last turn and head into the final stretch with Bob a distance in front of Jim. They are both running with the same velocity . When the finish line is a distance away from Jim, Jim accelerates at a constant until he catches up to Bob and passes him. Jim then continues at a constant speed until he reaches the finish line.
So there's two runners, Bob and Jim. You might want to draw a picture of them - pictures are always nice when trying to get your head around the situation.
Information we know about Bob:
Motion 1. He starts off at distance
ahead of Jim.
He is running at a velocity of
. He is not accelerating.
Information we know about Jim:
Motion 1. He starts off a distance
behind Bob.
He is initially running at a velocity of
. He is not accelerating.
Motion 2. When he is
away from the finish line, he accelerates
for a period of time.
Motion 3. He stops accelerating when he reaches and passes Bob.
Since this question is a bit more involved than I originally assumed and since I'm lazy, I'll only type up part a. It'll be good enough to give you the idea of what's going on anyway. I'd encourage an attempt at the rest of the question. I'm pretty sure there's a set of solutions for this practice exam, but I can't find it at the moment.
For reference, here are our equations of constant acceleration. You should already be familiar with these and become a pro at rearranging these to be able to figure out any of the values. As you do a lot of motion questions, you'll find that memorise them accidentally.
t)
Here, v is the final velocity, u is the initial velocity, a is the acceleration, t is the time, and x is the displacement.
You might come across different symbols used for these, common ones are also s for displacement/distance or
for initial velocity.
a) How long did it take Jim to catch Bob?
1. What are we looking for:Keyword: "How long", so we know that we are looking for a time. We are also talking about Motion 2 for Jim (in which he is accelerating.
2. What do we know already:For the sake of simplicity, we'll begin our modelling of the situation at t=0. We'll define this point to be the moment where Jim starts accelerating.
So we know that this is a bit after they've both been running at
, but since neither accelerated, there would still be a distance
between them.
The moment when Jim catches up to Bob, they will be at the same position. This moment will be at the same time for both. So, in other words
and
. Essentially what we will do is find out these values, and then solve for t to find out what time this occurred.
3. Selecting the equationsSo, for Jim we need an equation that involves
and
. We also know that he had an intial velocity of
and that he was accelerating in order to catch up. Looking back upon our six equations, we pick the one that fits all these values the best:
Therefore:
(I guess the subscript isn't necessary, but I like using them anyway)
For Bob, we know that his velocity was constant. From this we know his acceleration was zero. Again, we need an equation with
and
.
Our options are:
(can't use this, we don't know that much about his final velocity - would mean making assumptions or extra work)
(again final velocity)
This leaves:
Quite conveniently, since his acceleration is zero, we can get:
*t^2)
But the position information we have for Bob is a scalar - not a vector.
So, remembering that:
we can do this:
The value we have for Bob's initial position is 'd', so:
So to summarise, we have:
4. Now it's solving time! (no pun intended)And since:
and
Therefore:
Now we have to solve for t. This is going to be a bit messy, but this is what the question asks for (you won't get messy stuff like this in VCE Physics; blame the random MIT practice paper I found).
Rearrange:
(t) - d)
Notice this resembles a quadratic, it'd be fairly straightforward to solve for. I'm going to skip the rest, basically you'll end up with a formula for t (remember to reject the negative square root). It's not important anyway, I was mainly trying to show how you can get to answer when you're stuck.
So yeah, you really won't come across questions like this one in VCE, more often than not you'll be given values that you can quickly plug in to get an nice answer out. I chose this question because it's a good example for showing what to do when you're presented with a question you have no idea on - merely fall back on what the problem and the formulas tell you.
Of course, you have to keep a balance between using the equations and relying on the equations. If you become completely reliant on "plugging and chugging", you might find that you get stuck or overlook simple concepts. For example, the question might mention constant velocity and you might overlook the fact that acceleration would be zero in this situation.
As you progress through motion, you'll also cover stuff like energy, inclined planes, projectile motion, circular motion, gravitation etc. The approach remains the same (distill the information, apply concepts, apply the correct equation, profit). Become familiar with the equations and what they mean and suggest and you should be able to get through most questions. For understanding the concepts behind these equations, khanacademy.org has a good set of physics videos that covers pretty much all the motion stuff you'll come across.
This was a lot longer than expected. Hopefully it proved to be coherent and helpful. I also hope the example question I used doesn't scare anyone off; you won't get anything like that question in VCE Physics.
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