Question

The electromotive force for an electric circuit with a simplified generator is 𝐸(𝑡) 𝑣𝑜𝑙𝑡𝑠 at 𝑡 𝑠𝑒𝑐𝑜𝑛𝑑𝑠, where 𝐸(𝑡) = 50 𝑠𝑖𝑛120𝜋𝑡. Find the instantaneous rate of change of 𝐸(𝑡) with respect to 𝑡 at (a) 0.02 𝑠𝑒𝑐 and (b)0.2 𝑠𝑒c

Answer 1

Rate of change of the function is calculated as it's derivative so in this rate of change would be equal to $E'(t)=(50sin120\pi t)'=50\cdot120\pi\cdot cos120\pi t=6000\pi\cdot cos(120\pi t)$ . For t=0.02 instantaneous rate of change then is $6000\pi\cdot cos(120\pi \cdot0.02)=5824.833$ and for t=0.2 instantaneous rate of change then is $6000\pi\cdot cos(120\pi \cdot0.2)=18849.556$ .