2023HSCMultiple choice

Q9

1 mark

Question

A particle travels along a curve from $O$ to $E$ in the $xy$ -plane, as shown in the diagram. The position vector is $\mathbf r$ , velocity is $\mathbf v$ , and acceleration is $\mathbf a$ . While travelling from $O$ to $E$ , the particle is always slowing down. Which of the following is consistent with the motion?

A. $\mathbf r\cdot\mathbf v\le0$ and $\mathbf a\cdot\mathbf v\ge0$
B. $\mathbf r\cdot\mathbf v\le0$ and $\mathbf a\cdot\mathbf v\le0$
C. $\mathbf r\cdot\mathbf v\ge0$ and $\mathbf a\cdot\mathbf v\ge0$
D. $\mathbf r\cdot\mathbf v\ge0$ and $\mathbf a\cdot\mathbf v\le0$

Uncropped source page 7 for question 9; requires human review and cropping — Reviewed visual · source page 7

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Syllabus alignment

MechanicsVectors

Modelling motion without resistanceApply forces, Newton's laws and calculus to model straight-line motion without resistance.
Further operations with three-dimensional vectorsUse vector magnitude, unit vectors and scalar products to solve problems and prove geometric results.

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