To determine which of the given definitions are correct definitions for power, we need to understand that power is the rate at which work is done or energy is transferred. Mathematically, it is expressed as:
[tex]\[ \text{Power} = \frac{\text{Work}}{\text{Time}} \][/tex]
Additionally, when considering mechanical power, the formula can also be expressed in terms of force ([tex]\(F\)[/tex]), distance ([tex]\(d\)[/tex]), and time ([tex]\(t\)[/tex]):
[tex]\[ \text{Power} = \frac{F \cdot d}{t} \][/tex]
Let's evaluate each of the given options based on these correct definitions:
1. [tex]\(\text{work} \div \text{time}\)[/tex]:
This matches the definition [tex]\(\text{Power} = \frac{\text{Work}}{\text{Time}}\)[/tex]. Hence, this is correct.
2. [tex]\(\frac{\text{time}}{\text{work}} \)[/tex]:
This is the reciprocal of the correct definition and does not represent power. Hence, this is incorrect.
3. [tex]\(\frac{t}{F=d}\)[/tex]:
This notation does not make sense from a dimension analysis and is not a correct formula for power. Hence, this is incorrect.
4. [tex]\(\frac{F z t}{d}\)[/tex]:
This formula incorrectly multiplies force and time, which does not match any definition of power. Hence, this is incorrect.
5. [tex]\(\frac{F z d}{t}\)[/tex]:
This matches the definition [tex]\(\text{Power} = \frac{F \cdot d}{t}\)[/tex]. Hence, this is correct.
6. [tex]\(\frac{\text{work}}{\text{time}}\)[/tex]:
This is essentially the same as option 1 and matches the definition [tex]\(\text{Power} = \frac{\text{Work}}{\text{Time}}\)[/tex]. Hence, this is correct.
Based on these evaluations, the correct definitions for power are:
[tex]\[ [1, 6] \][/tex]
