Final Answer:
(a) For the object's total displacement to be zero at a later time t, it must have zero acceleration. (b) As t→∞ , the constant velocity indicates the object will persistently move eastward without any change.
Step-by-step explanation:
In the scenario where the total displacement at a later time t is required to be zero, the object needs to maintain a constant velocity. This implies zero acceleration (a=0). The definition of constant velocity is that the object is moving at a steady rate in a straight line, and any acceleration, whether positive or negative, would cause a change in velocity.
Now, consider the physical interpretation of the solution as t approaches infinity. With a constant velocity (v), the object will continue moving eastward indefinitely without any change. In the absence of acceleration, there won't be any deviation from the initial straight path. This scenario aligns with the notion that an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an external force, as described by Newton's first law of motion.
In summary, for the total displacement to be zero at a later time, the object must have zero acceleration, allowing it to sustain a constant velocity. As time approaches infinity, the object maintains this constant velocity, implying perpetual motion in the eastward direction.