Final answer:
The object in simple harmonic motion will move an additional 0.272 meters beyond the current displacement of 0.585 meters before it momentarily stops and starts to move back.
Step-by-step explanation:
To determine how much farther the object in simple harmonic motion (SHM) will move before it momentarily stops, we can use SHM equations. However, in the context of the given query, we do not need a complete kinetic analysis, as we are only asked to find the additional displacement before the object stops. At the point mentioned in the question - 0.585 m to the right of equilibrium with a velocity to the right and an acceleration to the left - the object is moving towards the maximum amplitude of its motion. Once it reaches this maximal point, the velocity will be zero. Since we already know the object's velocity and acceleration, we can use the kinematic equation for motion without time, v2 = u2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.
Given that the object has to stop, the final velocity v = 0, the initial velocity u = 2.10 m/s, and the acceleration a = -8.10 m/s2 (negative because it's opposite to the velocity). Solving the equation 0 = (2.10 m/s)2 + 2(-8.10 m/s2) · s for s, we find that s = 0.272 m.
Thus, the object will move an additional 0.272 meters from the point of 0.585 meters displacement before it momentarily stops.