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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 spe... 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 shows the correct acceleration, , we must consider the direction of the velocity, , and the nature of circular or curved motion. Given that the particle's speed is increasing, the acceleration must have a component that points towards the center of the curve to enable constant curvilinear motion.
In diagram B, the direction of the acceleration vector points towards the center of the curve (towards point B), which is consistent with the requirement for an object to follow a curved path. Therefore, it would allow the particle at point P to follow the curve to B.
In contrast, diagram A indicates that acceleration is directed away from the curve, which would not permit the particle to follow the curve effectively. Thus, the answer is:
B.