While no single method works for every problem, the following six-step strategy is widely applicable and encourages structured thinking:

Step 1: Examine the Situation

Determine which physical principles apply. Drawing a diagram or sketch helps conceptualize the problem and can guide your choice of coordinate system. Once the principles are identified, relevant equations can be chosen.

Step 2: Identify the Knowns

Make a list of all given information or what can be inferred. Phrases like “starts from rest” or “comes to a stop” indicate zero initial or final velocity, respectively. Often, initial time and position can be set to zero.

Step 3: Identify the Unknowns

Clearly state what needs to be found. In more complex problems, listing all unknowns and solving them sequentially may be necessary.

Step 4: Choose the Appropriate Equation(s)

Select equations that relate knowns to unknowns. Prefer equations with only one unknown. If an equation includes multiple unknowns, identify additional equations that can help.

Step 5: Solve and Include Units

Substitute the knowns into the equation, keeping units throughout the calculation. The result should have appropriate units and significant figures.

Step 6: Check for Reasonableness

Examine the magnitude, units, and sign of the result. Does the answer make physical sense? This step often reveals conceptual understanding.

These steps can be performed in different orders or simultaneously. With experience, they become more intuitive. To practice, work through the examples and attempt as many problems as possible, starting from simpler ones.

Physics describes nature. Sometimes, solving a problem yields a result that is mathematically correct but physically unreasonable. This happens when a premise is flawed or inconsistent.

For example, suppose a runner accelerates at:

[latex]a = 0.40~\text{m/s}^2[/latex]

for 100 seconds. Then:

[latex]v = v_0 + at = 0 + (0.40~\text{m/s}^2)(100~\text{s}) = 40~\text{m/s}[/latex]

Convert to miles per hour:

[latex]\left(\frac{40~\text{m}}{\text{s}}\right) \left(\frac{3.28~\text{ft}}{1~\text{m}}\right) \left(\frac{1~\text{mi}}{5280~\text{ft}}\right) \left(\frac{60~\text{s}}{1~\text{min}}\right) \left(\frac{60~\text{min}}{1~\text{hr}}\right) = 89~\text{mph}[/latex]

This speed is unrealistic for a human. Hence, one or more assumptions are flawed.

Strategies for Evaluating Reasonableness

Step 1: Solve Normally

Use standard steps and equations, such as:

[latex]v = v_0 + at[/latex]

Step 2: Assess the Answer

Ask whether the value is too large or small, has incorrect units or an incorrect sign. Convert to familiar units when needed.

Step 3: Identify the Issue

Determine whether unreasonable assumptions were made. In the running example, a 100-second acceleration at 0.40 m/s² is unlikely. The error lies in assuming such a long duration of steady acceleration.