To solve the question on identifying equivalent relationships based on the power formula [tex]\( \text{power} = \frac{\text{work}}{\text{time}} \)[/tex]:
1. Understand the given formula:
- Power ([tex]\( P \)[/tex]) is defined as work ([tex]\( W \)[/tex]) divided by time ([tex]\( T \)[/tex]).
- Thus, the formula is: [tex]\( P = \frac{W}{T} \)[/tex].
2. Rearrange the formula to solve for work:
- To find work in terms of power and time, multiply both sides of the equation by time ([tex]\( T \)[/tex]) to isolate work ([tex]\( W \)[/tex]):
- [tex]\( W = P \times T \)[/tex].
3. Rearrange the formula to solve for time:
- To find time in terms of work and power, divide both sides of the original formula by power ([tex]\( P \)[/tex]) to isolate time ([tex]\( T \)[/tex]):
- [tex]\( T = \frac{W}{P} \)[/tex].
Therefore, with these rearrangements, we obtain the two ways of stating the same relationship:
1. Work in terms of power and time:
- [tex]\( \text{work} = \text{power} \times \text{time} \)[/tex].
2. Time in terms of work and power:
- [tex]\( \text{time} = \frac{\text{work}}{\text{power}} \)[/tex].
So, the correct answers are:
- [tex]\( \text{work} = \text{power} \times \text{time} \)[/tex]
- [tex]\( \text{time} = \frac{\text{work}}{\text{power}} \)[/tex]
