A particle is travelling from A on the curve joining A to B - HSC - SSCE Mathematics Extension 2 - Question 9 - 2021 - Paper 1

To determine which diagram shows an appropriate acceleration that would allow the particle to follow the curve to B, we must consider the direction of the velocity and the necessary centripetal acceleration.

1. Understanding Velocity and Acceleration: At point P, the particle has a velocity vector $v$ directed along the curve towards point B. For the particle to continue along the curve while increasing its speed, the resultant acceleration must have a component that points towards the center of the curve (to maintain circular motion) and a tangential component that aligns with the increase in speed.

2. Analyzing Option A: In diagram A, the acceleration vector $a$ is directed towards point B from point P, which suggests a tangential acceleration without sufficient centripetal acceleration to keep the particle on the path. This would not allow the particle to effectively follow the curve as required.

3. Analyzing Option B: In diagram B, the acceleration vector $a$ is directed towards the center of the curve, which facilitates the necessary centripetal force while still maintaining the tangential component that contributes to the increase in speed.

4. Conclusion: Since option B allows for both the increase in speed (due to the tangential component of acceleration) and the curvature of the path (due to the centripetal component), it is the correct diagram that shows an appropriate acceleration for the particle at point P to follow the curve to B.