To determine the amount of work done by a motor, we can use the relationship between power, work, and time. The formula to calculate work is:
[tex]\[ \text{Work} = \text{Power} \times \text{Time} \][/tex]
Step-by-Step Solution:
1. Identify the given values:
- Power ([tex]\(P\)[/tex]): 5400 watts (W)
- Time ([tex]\(t\)[/tex]): 640 seconds (s)
2. Substitute these values into the formula:
[tex]\[ \text{Work} = 5400 \, \text{W} \times 640 \, \text{s} \][/tex]
3. Multiply the power by the time:
[tex]\[ \text{Work} = 5400 \times 640 \][/tex]
4. Calculate the product:
[tex]\[ \text{Work} = 3,456,000 \, \text{joules} \][/tex]
Thus, the work done by the motor in 640 seconds is 3,456,000 joules.
Now, let's compare this with the given options:
- 8.4 J
- 4,800 J
- 6,000 J
- 3,500,000 J
The closest option to our calculated work of 3,456,000 joules is 3,500,000 joules. Therefore, the correct answer is:
[tex]\[ \boxed{3,500,000 \, \text{J}} \][/tex]
