A cable pulls a box with force of 5 kN and raises it at the rate of `2 ms^(-1)`. What is the power of the engine providing tension to the cable?

Options

A. 2 Kw
B. `3.5 kW`
C. 5 kW
D. 10 kW

Explanation

To find the power of the engine providing tension to the cable, we can use the formula for power in the context of work done over time. The power (P) can be calculated using the formula:

\[ P = F \times v \]

where:
- \( P \) is the power,
- \( F \) is the force applied, and
- \( v \) is the velocity at which the object is being moved.

### Step-by-Step Solution:

1. **Identify the given values:**
- The force \( F \) exerted by the cable is 5 kN (kilonewtons).
- The velocity \( v \) at which the box is raised is 2 m/s.

2. **Convert the force from kilonewtons to newtons:**
- Since 1 kN = 1000 N, we convert 5 kN to newtons:
\[ F = 5 \, \text{kN} = 5 \times 1000 \, \text{N} = 5000 \, \text{N} \]

3. **Substitute the values into the power formula:**
\[ P = F \times v = 5000 \, \text{N} \times 2 \, \text{m/s} \]

4. **Calculate the power:**
\[ P = 10000 \, \text{W} = 10 \, \text{kW} \]

### Final Answer:
The power of the engine providing tension to the cable is **10 kW**.