A horizontal 50 N force acts on a 2 kg crate which is at rest on a smooth horizontal surface. At the instant the particle has gone 2 m, the rate at which the force is doing work is :

Options

A. (a)2.5 W
B. (b)25 W
C. (c)100 W
D. (d)500 W

Explanation

To solve the problem, we need to find the rate at which the force is doing work (power) when the crate has moved 2 meters. Here’s a step-by-step solution:

### Step 1: Identify the Given Information
- Force (F) = 50 N
- Mass (m) = 2 kg
- Displacement (s) = 2 m
- Initial velocity (u) = 0 m/s (the crate is at rest)

### Step 2: Calculate the Acceleration
Using Newton's second law of motion:
\[ F = ma \]
We can rearrange this to find acceleration (a):
\[ a = \frac{F}{m} \]
Substituting the values:
\[ a = \frac{50 \, \text{N}}{2 \, \text{kg}} = 25 \, \text{m/s}^2 \]

### Step 3: Use the Equation of Motion to Find Final Velocity
We will use the equation of motion:
\[ v^2 = u^2 + 2as \]
Substituting the known values:
\[ v^2 = 0 + 2 \times 25 \, \text{m/s}^2 \times 2 \, \text{m} \]
\[ v^2 = 100 \]
Taking the square root:
\[ v = \sqrt{100} = 10 \, \text{m/s} \]

### Step 4: Calculate the Power
Power (P) is defined as the rate at which work is done, which can be calculated using the formula:
\[ P = F \times v \]
Substituting the values:
\[ P = 50 \, \text{N} \times 10 \, \text{m/s} \]
\[ P = 500 \, \text{W} \]

### Conclusion
The rate at which the force is doing work when the crate has moved 2 meters is **500 Watts**.

---