The correct option is (c).
Explanation
Power is defined as the time rate at which work is done or energy is transferred. It measures how fast a task is completed. The mathematical expression for average power is $P = \frac{W}{t}$, where $W$ is the work done and $t$ is the time interval.- Statement 1 is correct: Power is a scalar quantity. Although it is related to force (a vector) and velocity (a vector) through the dot product ($P = \vec{F} \cdot \vec{v}$), the result is a scalar. Additionally, since work and time are both scalars, their ratio is also scalar. It has magnitude but no specific direction.
- Statement 2 is incorrect: Power is dependent on the time taken to complete a task. According to the formula $P = \frac{W}{t}$, power is inversely proportional to time. If the same amount of work is done in less time, the power generated is greater. Conversely, if it takes more time, the power is less.
- Statement 3 is correct: The SI unit of power is the Watt (W). One Watt is defined as the consumption or transfer of energy at the rate of one Joule per second ($1 \text{ W} = 1 \text{ J/s}$). Therefore, one kilowatt ($1 \text{ kW}$), which equals $1000 \text{ Watts}$, is equal to 1000 Joules per second.
Key Takeaway: Power is the rate of doing work ($P = W/t$). It is a scalar quantity, and its SI unit is the Watt ($1 \text{ W} = 1 \text{ J/s}$).