Photo AI
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 the correct diagram, we must understand that for a particle moving along a curved path with increasing speed, the acceleration must have two components:
- Tangential Acceleration: This is due to the increase in the speed of the particle, acting along the direction of the velocity vector.
- Centripetal Acceleration: This is necessary to keep the particle moving along the curve and is directed towards the center of the curvature.
In the context of the diagrams provided:
- Diagram A shows the acceleration vector directed away from the curve, which will not facilitate the particle’s movement along the curve toward B.
- Diagram B shows the acceleration vector directed towards the center of curvature while having a component in the direction of the velocity, which allows the particle to both accelerate and change direction suitably.
Thus, the correct answer is Diagram B, as it provides the necessary centripetal acceleration along with tangential acceleration for the particle to follow the curve to B.