A body of mass `0.4kg` starting at origin at `t=0` with a speed of `10ms^(-1)` in the positive x-axis direction is subjected to a constant `F=8` N towards negative x-axis.

Options

A. `-6000m`
B. `-8000m`
C. `+4000m`
D. `+7000m`

Explanation

To solve the problem step by step, we will follow the laws of motion and apply the relevant equations.

### Given Data:
- Mass of the body, \( m = 0.4 \, \text{kg} \)
- Initial velocity, \( u = 10 \, \text{m/s} \) (in the positive x-direction)
- Force acting on the body, \( F = -8 \, \text{N} \) (towards the negative x-direction)
- Time, \( t = 25 \, \text{s} \)

### Step 1: Calculate Acceleration
Using Newton's second law of motion, we can calculate the acceleration \( a \) using the formula:
\[ F = m \cdot a \implies a = \frac{F}{m} \]
Substituting the values:
\[ a = \frac{-8 \, \text{N}}{0.4 \, \text{kg}} = -20 \, \text{m/s}^2 \]
The negative sign indicates that the acceleration is in the opposite direction to the initial velocity.

### Step 2: Calculate Displacement
We will use the equation of motion to calculate the displacement \( s \):
\[ s = ut + \frac{1}{2} a t^2 \]
Substituting the values:
\[ s = (10 \, \text{m/s})(25 \, \text{s}) + \frac{1}{2} (-20 \, \text{m/s}^2)(25 \, \text{s})^2 \]
Calculating each term:
1. \( ut = 10 \times 25 = 250 \, \text{m} \)
2. \( \frac{1}{2} a t^2 = \frac{1}{2} \times (-20) \times (25^2) = -10 \times 625 = -6250 \, \text{m} \)

Now substituting back into the displacement equation:
\[ s = 250 - 6250 = -6000 \, \text{m} \]

### Conclusion
The displacement of the body after 25 seconds is \( -6000 \, \text{m} \), indicating that the body has moved 6000 meters in the negative x-direction.

### Final Answer
The displacement is \( -6000 \, \text{m} \).

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