Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions. This topic is shared by Calculus AB and Calculus BC.
Understanding
- I can explain velocity as the rate of change of position and acceleration as the rate of change of velocity, with units. (Guide: “Position, velocity and acceleration”; Practice Q6(a))
- I can explain the difference between velocity and speed. (Guide: “Direction of motion”; Practice Q6(c))
- I can explain why v = 0 does not always mean a change of direction. (Guide: “Direction of motion”; Practice Q7(b))
- I can explain the difference between displacement and total distance travelled. (Guide: “Displacement and total distance”; Practice Q4)
Skills
- I can find v(t) and a(t) from x(t), including with the product rule. (Guide: Worked example 1; Practice Q1, Q7(a))
- I can use a sign analysis of v(t) to find when an object moves in each direction. (Guide: Worked example 1; Practice Q7(b))
- I can read acceleration and speed from a velocity graph. (Guide: Worked example 2 and Figure 2)
- I can estimate acceleration from a velocity table, and find an average acceleration. (Practice Q5(a), Q5(d))
- I can find total distance by splitting time at the turning points. (Guide: Worked example 1 and Figure 1; Practice Q4, Q7(d))
- I can use a graphing calculator to find when an object reaches a position, and its speed then. (Practice Q6(c))
Reasoning
- I can decide whether an object is speeding up or slowing down by comparing the signs of v and a, and say so in a sentence. (Guide: “Speeding up and slowing down”; Practice Q2, Q3, Q6(d), Q7(c))
- I can use the Intermediate Value Theorem to show an object must be at rest at some time. (Practice Q5(b))
- I can justify a greatest height using the sign change of velocity. (Practice Q6(b))
All ticked? Move on to Topic 4.3, Rates of Change in Applied Contexts Other Than Motion, or return to the Calculus AB roadmap or the Calculus BC roadmap.