The energy of a system increases at a rate of 3.5 t + 6.2 t², in joules.What is the instantaneous power at t = 3.1 s? A)3.5 W B)6.2 W C)16 W D)42 W E)70 W

Question

Quizplus · Accepted Answer

The instantaneous power is given by the derivative of the energy with respect to time. The given energy function is $3.5t + 6.2$, so its derivative with respect to time $t$ is $3.5$. To find the instantaneous power at $t = 3.1$ s, we substitute $t = 3.1$ into the derivative, but since the derivative is a constant $3.5$, the instantaneous power is simply $3.5 + 6.2 = 9.7$ W. However, there seems to be a misunderstanding in the interpretation of the given function due to formatting issues. Assuming the correct interpretation involves a time-dependent term, and the question aims for the calculation at a specific time, the correct approach involves directly evaluating or differentiating the given expression correctly. Given the formatting issue, let's correct the approach: if the energy increases at a rate of $3.5t + 6.2$, and assuming the correct interpretation involves differentiation, the power at $t = 3.1$ s would indeed involve calculating with these values directly. However, without a clear, correctly formatted expression, the precise calculation might differ. The correct choice should be based on the derivative of the energy function, which represents power. Without the exact operation due to formatting, the intended correct answer and explanation might involve a misunderstanding of the provided expression.

The Energy of a System Increases at a Rate of 3.5