Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions.
Understanding
- I can explain what makes a force resistive, give the direction of F_r = −kv for any velocity, and state the unit of k. (Guide: “What makes a force resistive”)
- I can explain why the constant-acceleration equations do not apply when a resistive force acts. (Guide: Worked example 1)
- I can explain terminal velocity as zero net force, not zero force, and say why an object thrown faster than v_T slows down. (Guide: “Terminal velocity”; Practice Q3)
Calculation
- I can find the terminal velocity and the time constant τ = m/k from the forces. (Guide: Worked example 2; Practice Q1)
- I can write Newton’s second law as a differential equation, with signs that match my axis, for coasting, falling and rising objects. (Guide: “Newton’s second law becomes a differential equation”; Practice Q4(a))
- I can separate variables and integrate between matching limits to find v(t). (Guide: “Separation of variables”; Practice Q4(b), Q5(b))
- I can find a(t) by differentiating v(t), and x(t) by integrating with the initial position, including the finite coasting distance mv₀/k. (Guide: Worked example 1; Practice Q5(c), Q6(d))
- I can find the time to reach a given speed using logarithms, such as the halving time τ ln 2. (Guide: Worked example 1(c); Practice Q4(c))
Reasoning
- I can sketch v–t and a–t graphs, showing the initial slope, the asymptote and the time constant. (Guide: Figure 1; Practice Q2, Q5(d))
- I can linearise velocity data with ln v against t to test the model and extract k. (Practice Q6)
- I can compare two objects with the same k but different masses at release and at later times. (Practice Q7)
All ticked? Move on to Topic 2.10, Circular Motion, or return to the course roadmap.