Here is a brief outline of an (almost) fail-safe problem solving method

· READ THE QUESTION

· IDENTIFY THE INFORMATION GIVEN TO YOU

o Look for key words like increasing; it’s speed, at time, etc.

· LOOK FOR THE UNKNOWNS

o Look for questions asking, at what time, what is, where is, etc.

· WRITE DOWN YOUR KNOWN AND UNKNOWN QUANTITIES

o Make sure you differentiate between different objects in the problem, for example v_{icar, I} for a cars initial velocity. This will make sure you don’t get these values confused in your calculations.

· LOOK FOR EQUATIONS RELATING YOUR KNOWN QUANTITIES TO THE UNKNOWN QUANTITIES

o While some questions are tricky, typically there won’t be many trick questions. Therefore, everything you need to solve a problem will be given to you.

· SOLVE THESE EQUATIONS FOR THE UNKNOWN QUANTITIES
WITHOUT PLUGGING IN NUMBERS

o Plugging in numbers too early can lead to many mistakes. The only exception is if a number is zero, then just remove that variable from the equation it appears in.

· SIMPLIFY THE EQUATIONS AS MUCH AS POSSIBLE.

o Sometimes a big mess can turn into something small, as will be seen in the sample problem in section 2

· PLUG IN YOUR NUMBERS AND SOLVE THE PROBLEM

o If the number seems reasonable, keep it, if not look for errors and try again. This is another reason why plugging in numbers too early is a bad idea, if you plug in numbers, sometimes you won’t see what steps you took to get to your final answer.

I hope this helps a little, if you have any questions or if the example in section 2 wasn’t clear enough come see me during my tutoring sessions and I will go over it with you.

-Sam

The main thing to do with any physics problem is to READ THE QUESTION and pick out the information you are given.

EXAMPLE:

from chapter 2 of Halliday/Resnick/Walker 8^th ed.

-At the instant the traffic light turns green, an automobile starts with a constant acceleration of 2.2 m/s². At the same instant a truck, traveling with a constant speed of 9.5 m/s overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the automobile be traveling at that instant?

The first thing to notice:

Most of the words in this problem don’t mean anything; they are just trying to help you visualize what is going on. The first question to ask is: What important information is the author trying to tell me?

· Look for terms like: constant, decreasing, increasing, or any other word describing position or motion.

o Constant acceleration of 2.2m/s².

§ This tells you that the acceleration of the car will be used in finding the answer.

o Constant speed of 9.5 m/s.

§ This will also be important…

o Overtakes and passes

§ So at the time mentioned, these objects are next to each other.

· Look for the questions:

o How far beyond… etc.

§ Here we are looking for a distance

o How fast …

§ Looking for a speed

· Write down the known information for all objects in question

o For the car: v_i=0, a_ir=2.2m/s²

o For the truck: v_i=9.5m/s, a=0

o You want to be sure you can tell the difference between your initial and final values in the problem.

· Write down your unknown information

o Car: x_final , v_final

o Truck: x_final

· Look for equations containing these variables.

o This is the part that can give people the most trouble, I recommend that you make a list of the formulas you are given in class to use on your homework. Also, try to make copies of any formula sheets your professor gives you for a test as these are usually clear and have all the information you need on them.

o Back to the formulas, you will find that the equations containing these variables are:

§ x_f=x_i+v_it+.5at²

§ v_f=v_i+at

These are the only two formulas you need to find the answer to this problem. Now the trick is to get them into a form you can actually use….

· Equations for the car:

Known: initial position (always call this zero unless the book specifies otherwise), acceleration (given), initial velocity (at rest means this is zero)

Unknown: final position, final velocity, time

o How can these equations be rearranged to eliminate at least one of the unknowns? Try to find an unknown that the question does not ask about and solve one of the equations for it.

§ We don’t need to know the time, so look at the velocity formula. Rearrange that to solve for time and we have:

t=(v_f-v_i)/a

x_f=x_i+v_it+.5at²

plug in your formula for t to get:

x_f=x_i+v_i(v_f-v_i)/a+.5a((v_f-v_i)/a)²

Remembering that initial velocity and position are zero:

x_f=.5a(v_f/a)²=.5v_f²/a

x_f=.5v_f²/a

looks much better doesn’t it…

· Truck equations:

Known: initial velocity (given), initial position (zero, same as above), acceleration (constant velocity means acceleration is zero)

Unknown: final position, time

o We don’t care to find the final velocity, since the velocity is constant, so all we need is the final position.

§ x_f=x_i+v_truckt+.5at²

initial position is zero, acceleration is zero so:

§ x_f=v_truckt

· Now that all the equations are there we just need to notice that the final position and the time, since the problem asks at what position will the car pass the truck, will be the same for both vehicles, so if you make the two equations equal to each other, you can solve for the final velocity of the car.

· v_truck(v_f,car/a_car)=.5v_f²/a, so

v_f,car=2v_truck

· now we can solve for the distance,

o x_f=.5v_f²/a=.5(2v_truck)²/a

o x_f=5(2v_truck)²/a

Please remember that working with these equations takes some practice. Don’t get frustrated if this looks confusing, just try to take it step by step.

I can almost guarantee that if you use this type of sytematic approach to every homework question you will do great on your homework and be extremely well prepared for your tests. I am available to go over this method with you during my tutoring hours, the times are available on: