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How long does it take a [tex][tex]$1.51 \times 10^4 \, W$[/tex][/tex] steam engine to do [tex][tex]$8.72 \times 10^6 \, J$[/tex][/tex] of work? Round your answer to three significant figures.

A. [tex][tex]$1.02 \times 10^1 \, s$[/tex][/tex]
B. [tex][tex]$5.77 \times 10^2 \, s$[/tex][/tex]
C. [tex][tex]$7.21 \times 10^5 \, s$[/tex][/tex]
D. [tex][tex]$1.32 \times 10^{11} \, s$[/tex][/tex]



Answer :

GinnyAnswer
To determine the time it takes for a steam engine with a power output of [tex]\(1.51 \times 10^4\)[/tex] watts to do [tex]\(8.72 \times 10^6\)[/tex] joules of work, we need to use the relationship between work, power, and time. The relevant formula to use is:

[tex]\[ \text{Power} = \frac{\text{Work}}{\text{Time}} \][/tex]

Solving for time:

[tex]\[ \text{Time} = \frac{\text{Work}}{\text{Power}} \][/tex]

1. Identify the given values:
- Power ([tex]\(P\)[/tex]): [tex]\(1.51 \times 10^4\)[/tex] W
- Work ([tex]\(W\)[/tex]): [tex]\(8.72 \times 10^6\)[/tex] J

2. Substitute the given values into the equation:

[tex]\[ \text{Time} = \frac{8.72 \times 10^6 \, \text{J}}{1.51 \times 10^4 \, \text{W}} \][/tex]

3. Compute the division:

[tex]\[ \text{Time} = \frac{8.72 \times 10^6}{1.51 \times 10^4} \][/tex]
[tex]\[ \text{Time} \approx 577.483 \, \text{s} \][/tex]

4. Round the answer to three significant figures:

[tex]\[ \text{Time} \approx 577 \, \text{s} \][/tex]

Therefore, the time it takes for the steam engine to do the work is approximately [tex]\(5.77 \times 10^2\)[/tex] seconds.

So the correct answer is:
[tex]\[ \boxed{5.77 \times 10^2 \, \text{s}} \][/tex]

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