Final answer:
The current reverses direction for the first time when the magnet is centered in the plane of the coil, which occurs at some point not specified in the provided data. Exact timing is needed to determine the precise moment.
Step-by-step explanation:
The question concerns the moment when the electric current reverses direction in a situation where a magnet is moving relative to a coil, inducing an electromotive force and subsequent current flow, which is a topic covered in Physics. Given that the current decreases by a factor of 0.368 in each time interval, we can determine when the current changes direction based on the provided information and the behavior of induced currents.
The current first falls to 0.368 of its initial value after 2.50 ms, which means it would be 3.68 A at that moment (assuming an initial current of 10.0 A). Then, in another 2.50 ms (totally 5.00 ms), it declines to 0.368 of that value again. To find the moment when the current reverses for the first time, we need to look for when it becomes zero and then starts flowing in the opposite direction. This occurs when the magnet is centered in the plane of the coil as per the information provided.
Thus, the current reverses direction for the first time when the magnet is centered in the plane of the coil, which would be at some point between the described declines in current. The exact moment, however, cannot be determined without more specific information about the timing of the magnet's movement with respect to the coil.