Question

how long does it take a ( 1.51 \times 10^4 ) w steam engine to do ( 8.72 \times 10^6 ) j of work? round your answer to three significant figures.
( \bigcirc 1.02 \times 10^1 ) s
( \bigcirc 5.77 \times 10^2 ) s
( \bigcirc 7.21 \times 10^8 ) s
( \bigcirc 1.32 \times 10^{11} ) s

Explanation:

Step1: Recall the power formula

Power $P$ is defined as work $W$ done per unit time $t$, so the formula is $P=\frac{W}{t}$. We can rearrange this formula to solve for time: $t = \frac{W}{P}$.

Step2: Substitute the given values

We are given that $P = 1.51\times 10^{4}\text{ W}$ and $W=8.72\times 10^{6}\text{ J}$. Substituting these values into the formula for time, we get $t=\frac{8.72\times 10^{6}\text{ J}}{1.51\times 10^{4}\text{ W}}$.

Step3: Perform the division

When dividing numbers in scientific notation, we divide the coefficients and subtract the exponents of 10. So, $\frac{8.72}{1.51}\approx 5.77$ and $\frac{10^{6}}{10^{4}} = 10^{6 - 4}=10^{2}$. Combining these results, we get $t\approx 5.77\times 10^{2}\text{ s}$.

Answer:

$5.77\times 10^{2}\text{ s}$