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A particle is travelling from A on the curve joining A to B - HSC - SSCE Mathematics Extension 2 - Question 9 - 2021 - Paper 1
Question 9
A particle is travelling from A on the curve joining A to B. At a particular time, the particle is at point P and has velocity v, as shown in the diagram. The speed... show full transcript
Worked Solution & Example Answer:A particle is travelling from A on the curve joining A to B - HSC - SSCE Mathematics Extension 2 - Question 9 - 2021 - Paper 1
Step 1
Which of the following diagrams shows an acceleration, a, which would allow the particle to follow the curve to B?
Answer
To determine which diagram correctly represents the required acceleration for the particle at point P, we must consider both the velocity direction and the nature of the motion. The particle travels along a curved path from A to B, and since the speed is increasing, the acceleration must have a component in the direction of the velocity.
In Diagram B, the acceleration vector points towards the center of the curvature, which is essential for changing the direction of the velocity. Additionally, the upward component of the acceleration in Diagram B also supports the increase in speed as the particle moves towards B. Therefore, this diagram correctly shows the necessary acceleration for the particle to follow the curve.
Hence, the answer is B.