Key idea
After studying problem solving with units and assumptions, check whether you can explain your answer without notes and apply the idea to an unfamiliar situation.
Choose a physical model before an equation
For engineering problems, sketch the system, list known values and unknowns, and state your assumptions. An equation can be mathematically correct and still be inappropriate for the physical process in the question.
Distance divided by elapsed time gives average speed; it describes speed throughout an interval only under a constant-speed assumption.
Use units as an error-detection tool
Before substituting values, express quantities in compatible units. A vehicle covering 120 m in 10 s has a speed of 12 m/s in this example. Converting with a factor of 3.6 gives 43.2 km/h.
Check dimensions: metres per second represent speed, whereas metres per second squared describe acceleration. If the units of the answer do not match the requested quantity, inspect the model, not just the arithmetic.
Worked kinematics problem and independent check
A moving object maintains 12 m/s for 10 s, so it covers 120 m. Another 5 s at the same speed adds 60 m. Total distance is 180 m over 15 s.
Check by dividing 180 m by 15 s to recover 12 m/s. The position-time graph has a constant slope in the assumed model. Additional distance over more time does not itself imply acceleration.
What changes when motion is not uniform
If the problem instead specifies acceleration from rest, a single constant-speed equation will not describe the entire motion. Review the appropriate acceleration model and initial conditions.
Deliberately changing one assumption is an effective way of checking whether you understand why the original solution worked.
Try it yourself
Worked example: speed, distance, and unit conversion
A vehicle travels 120 m in 10 s at constant speed, then keeps moving at that speed for another 5 s.
- 1State the model: uniform motion; the question does not specify acceleration.
- 2Compute speed: 120 m / 10 s = 12 m/s. Convert using 12 × 3.6 = 43.2 km/h.
- 3Find the extra distance: 12 m/s × 5 s = 60 m, making the total 180 m.
- 4Check using the full interval: 180 m / 15 s = 12 m/s. A position-time sketch would have a constant slope.
How to check your work
The numerical results and units are consistent under constant-speed assumptions. A nonuniform motion model would require different reasoning.
Common mistakes
Mistaking recognition for mastery
Substituting numbers into equations without checking units or the assumptions that make the formula valid.
Practicing only repeated examples
A familiar example can be reproduced from memory. Changing conditions tests understanding.
Ignoring course sources
Required terminology, depth, and procedures depend on your syllabus.
Frequently asked questions
Where should I start?
Review your syllabus, separate learning objectives, work through one unit, and end with questions answered without notes.
How should I schedule review?
Mix current and older questions, prioritize mistakes, and adjust the schedule to difficulty.
Are flashcards enough?
Flashcards can test short facts and distinctions. Add cases and problems to assess application.
Sources and further reading
References on learning strategies. The original activities in this guide are educational examples and should be checked against your course materials.