Reflective Mental Overseer Questions:
- What method will I use to solve the relevant physics equations for the unknowns ?
    Purely Numerical Approach
    Purely Symbolic Approach
    Combined Numerical and Symbolic Approach
    Calculator's Solve Mode
    Graphing Calculator Approach

Purely Numerical Approach
Action:
- Substitute the numerical values of all the known quantities into the relevant physics equations first, and then solve the resulting equations for any unknowns. It is advisable to convert the knowns into SI units before you substitute them into the relevant physics equations or else your resulting answer will not be in the units you expect.

Comments:
- The advantage of this method is that it is usually faster because it reduces complicated equations to simpler equations that can be more easily manipulated. It is also easier to see what quantities are unknown.

- The disadvantage of this method is that it is harder to both locate and correct any errors.

- Once you have solved a problem using numbers, you have an opportunity to go back and retrace your steps using symbols.

Purely Symbolic Approach
Action:
- Leave all knowns as symbols and solve for any unknowns as an equation in which the "unknown = expression of the knowns", one equation for each unknown. Then substitute the values of the knowns into the resulting the bottom line equation to determine the value of an unknown.

Comments:
- The advantage of this method is that it is easier to retrace the logic of the steps you used to solve the problem.

- Once a symbolic solution is determined, you do not need to resolve the problem for a change in the input values. You only need to substitute the new values into the final equation.

- Symbols are easier to write down and manipulate than numbers because they take less strokes to write down and are smaller in size than the numbers they represent.

Combined Numerical and Symbolic Method
Rather than use either a purely numerical approach or purely symbolic approach exclusively, it is often better to use a combination of the two processes.

Action:
- Focus on some important quantities whose values are unknown but would be useful to know, quantities that you can see how to find. Solve for them symbolically and then determine their numerical values. Then use these as new knowns to reformulate the problem into a new problem requesting the same unknowns but with more givens, namely the values you just determined.

Comments:
- The advantage of this approach is that you break the problem down into smaller chunks which can be more easily manipulated.

- Another advantage is that you get to see the numerical values of certain intermediate quantities. Many times you can tell if their values seem reasonable.

Using a Calculator's Solve Mode
Another method is to use the "solve mode" of your calculator. The exact procedure varies from calculator to calculator. You will need to refer to your calculator's manual. The general approach is to first enter the relevant physics equation symbolically. Next enter the values of the known variables in that equation. Put in a guess for the unknown and then "hit" the solver button to find the unknown.

Comments:
- One advantage is that this method is fast once you have learned how to use the solver.

- There are some problems that cannot easily be solved symbolically, or even solved at all symbolically.

- The disadvantage of this method is that if you make an error, you will not know it unless your answer looks unreasonable. For example, if you do not enter all the known values in SI units, then your calculator will give you a number but it will not be dimensionally correct.

- There are disadvantages associated with the algorithms that your calculator uses to solve the equation for the unknown. For example, the equation may have more than one solution and the solution your calculator returns may not be the one you are seeking.

-This method will work only if the equation you are using has only one variable that is unknown.

- Another disadvantage is that you lose touch with the problem-solving process. If you do not practice solving equations, then it becomes much harder to manipulate the relevant generic equations to generate an equation that you can put into your calculator to solve in the first place.

- This is a good method to use to double-check a symbolic solution.

Using a Graphing Calculator
Often it useful to plot the relevant physics equation(s) on a graphing calculator. Many times this can be done before manipulating any of the equations first. After plotting the equations one can sometimes just look at the graph and "visually figure out" the answer.

Example:
A speeding station wagon moving at a constant speed of 88.0 km/hr passes a parked police car. If the police car starts accelerating uniformly at 3.00 m/s² from the moment the wagon passes the police car, how long will it take the police car to catch the station wagon ?

Plotting both the distance traveled by the station wagon and the distance traveled by police car on the same graph, we can see that where the two curves cross is the point where the police car catches up with the wagon. From the graph, we could also find the distance and the time it took for the police car to catch the wagon. Note that the graph on the right is only a schematic representation of what the plot would actually look like on your calculator.

Comments:
- The visual display of a graph is extremely helpful in seeing what is taking place with the variables in a problem.

- When I get stuck in solving a problem, I will often plot up some of the relations that I believe are true. Seeing the graph, I can often tell if I am on the right track. If I am on the right track the structure of the graph will sometimes give me new insight into how to solve for a requested unknown.