A particle travels along a curve from O to E in the xy-plane, as shown in the diagram - HSC - SSCE Mathematics Extension 2 - Question 9 - 2023 - Paper 1

To analyze the motion of the particle, we note that since it is slowing down, the acceleration vector must point in a direction against the velocity vector. This means that the dot product of acceleration and velocity must be non-positive:

$a · v ≤ 0.$

Since the particle moves in the positive direction of the curve from O to E, we can conclude that the position vector r and the velocity vector v will have a positive dot product:

$r · v ≥ 0.$

Thus, the condition that matches the description of the particle's motion is option D:

• r · v ≥ 0 and a · v ≤ 0.