Final answer:
In physics, the greatest instantaneous velocity for a particle motion, indicated by zero acceleration, is at t = 2s with a velocity of 20 m/s. The velocity becomes zero and negative as the acceleration changes from positive to negative, representing deceleration and a reversal in motion direction.
Step-by-step explanation:
The subject matter in question pertains to the analysis of a particle's motion in physics, specifically identifying aspects related to its velocity and acceleration. When asked to identify the time at which the instantaneous velocity is greatest, one must consider both the numerical and graphical analysis of the particle's motion. At time t = 2s, the particle achieves its maximum velocity of 20 m/s, which coincides with the acceleration being zero. This marks the point where the velocity function has a slope of zero, indicating a local maximum for the velocity.
To ascertain the time at which the velocity is zero or negative, one must look at the change of the acceleration sign. As the acceleration decreases past zero to become negative, the velocity, which was at its maximum, begins to decrease until it reaches zero and eventually becomes negative, suggesting a change in the direction of motion. This is analogous to a real-world scenario where a car accelerates to its top speed before decelerating, stopping, and possibly reversing direction.