Final answer:
To calculate the electric current in the metallic wire at t=0.1 second, we take the derivative of the given charge function Q(t) with respect to time t and evaluate at the specific time. Applying calculus concepts such as the product rule and chain rule is necessary for this physics question.
Step-by-step explanation:
The student's question involves finding the electric current in a metallic wire at a given time when the charge as a function of time, Q(t), is known. In this case, the electric current, I, is the rate of change of charge with respect to time, given by the derivative of Q(t) with respect to t. Specifically, for the function Q=3.0e^{-t} \sin(2t^2 +1) Coulombs, the current at time t=0.1 seconds is calculated using the derivative:
I(t) = \frac{dQ}{dt}
At t=0.1 seconds, taking the derivative of the provided Q(t) function and evaluating at t=0.1, we can find the instantaneous current. This involves applying the product rule for derivatives and the chain rule for the composition of functions within the sine function.
Do note that this question is a direct application of calculus in physics, making it an interdisciplinary problem at a high school or introductory college level. The aim is to link the theoretical concept of derivatives to a practical physical concept: electric current in a metallic conductor.