Reading & writing · Grades 11–12
The right formula, the wrong model
Read once, answer together, and check your reasoning.
The right formula, the wrong model
A learner correctly substitutes numbers into a constant-acceleration formula to estimate a vehicle’s travel distance. The recorded velocity data, however, show that acceleration changes sharply during the journey. The arithmetic is sound, but the model’s condition is not satisfied. The teacher asks the learner to use smaller intervals or another method consistent with the data rather than merely rechecking multiplication.
Try it yourself
Why is correct arithmetic insufficient in this example?
What evidence conflicts with the assumption?
Why might smaller intervals help?
State the broader lesson for using formula sheets.
Check your understanding
Answers and marking notes
- The chosen formula assumes constant acceleration, which the data do not support over the whole journey.
The chosen formula assumes constant acceleration, which the data do not support over the whole journey.
- The recorded velocity data indicate sharply changing acceleration.
The recorded velocity data indicate sharply changing acceleration.
- Acceleration may be approximately constant over shorter intervals, but this approximation must be checked.
Acceleration may be approximately constant over shorter intervals, but this approximation must be checked.
- Check variables, units, domain restrictions and modelling conditions before substituting numbers.
Check variables, units, domain restrictions and modelling conditions before substituting numbers.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.