Explanation:
When work is done at a faster rate, the power is increased. This can be understood through the following points:
Definition of Power:
- Power is defined as the rate at which work is done or the amount of work done per unit of time.
- Mathematically, power is calculated as P = W/t, where P is power, W is work, and t is time.
Relationship between Power and Work:
- Power is directly proportional to work.
- When work is done at a faster rate (i.e., completing the same amount of work in less time), the power increases.
- Conversely, if work is done at a slower rate (i.e., completing the same amount of work in more time), the power decreases.
Implications:
- If work is done at a faster rate, it means that more power is being exerted.
- This could be achieved by either applying a greater force or by completing the work in less time.
Therefore, the correct answer is option A: power is more.

Explanation:
In order to understand why power is more when work is done at a faster rate, it is important to first understand the concept of power and its relation to work.

Power:
Power is the rate at which work is done or energy is transferred. It is defined as the amount of work done per unit time. Mathematically, power can be expressed as:

Power = Work / Time

Work:
Work is the transfer of energy that occurs when a force is applied to an object and the object is displaced. It is given by the formula:

Work = Force x Displacement x cos(angle)

Relation between Power and Work:
From the formula for power, we can see that power is directly proportional to work. This means that when more work is done, the power is greater. Similarly, when less work is done, the power is less. Therefore, if work is done at a faster rate, it means that more work is being done in a given amount of time, resulting in greater power.

Example:
Let's consider an example to illustrate this concept. Suppose two people are lifting the same object to the same height. The first person takes 10 seconds to lift the object, while the second person takes only 5 seconds to lift the same object to the same height. Both individuals are doing the same amount of work (assuming the force applied and displacement are the same), but the second person is doing the work at a faster rate than the first person. Therefore, the second person has a higher power output compared to the first person.

Conclusion:
In conclusion, when work is done at a faster rate, power is more. This is because power is directly proportional to the amount of work done, and when work is done more quickly, more work is done in a given amount of time, resulting in a higher power output.