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 the correct diagram that allows the particle to follow the curve, we must consider the direction of the velocity vector $v$ at point P and the nature of the acceleration vector $a$.

1. Understanding Velocity and Acceleration:

   • At point P, the particle has a velocity directed tangentially along the curve towards point B.
   • Since the speed is increasing, the acceleration must have a component in the direction of the velocity to ensure the particle accelerates along the path.

2. Analyzing Diagram A:

   • Diagram A shows acceleration $a$ directed upwards and slightly towards point B. However, this direction primarily affects the change in speed but not in maintaining the curvature of the path.

3. Analyzing Diagram B:

   • Diagram B shows acceleration $a$ directed to the left, which aligns it with the inward direction, allowing it to follow the curvature of the path leading towards point B.

Thus, the appropriate choice is B, as it demonstrates the necessary inward acceleration that enables the particle to continue moving along the curve while increasing its speed.