A body of mass 5kg moves under a force of `10hati+10hatj-20hatk`. What is the acceleration produced?

Answer

To find the acceleration produced by a force acting on a body, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. Mathematically, this can be expressed as:

\[ \mathbf{F} = m \cdot \mathbf{a} \]

Where:
- \( \mathbf{F} \) is the force vector,
- \( m \) is the mass of the body,
- \( \mathbf{a} \) is the acceleration vector.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Mass of the body, \( m = 5 \, \text{kg} \)
- Force vector, \( \mathbf{F} = 10 \hat{i} + 10 \hat{j} - 20 \hat{k} \, \text{N} \)

2. **Use Newton's Second Law**:
According to Newton's second law, we can express acceleration as:
\[ \mathbf{a} = \frac{\mathbf{F}}{m} \]

3. **Substitute the Values**:
Substitute the force vector and the mass into the equation:
\[ \mathbf{a} = \frac{10 \hat{i} + 10 \hat{j} - 20 \hat{k}}{5} \]

4. **Divide Each Component by Mass**:
Now, divide each component of the force vector by the mass:
\[ \mathbf{a} = \left( \frac{10}{5} \hat{i} + \frac{10}{5} \hat{j} + \frac{-20}{5} \hat{k} \right) \]
This simplifies to:
\[ \mathbf{a} = 2 \hat{i} + 2 \hat{j} - 4 \hat{k} \, \text{m/s}^2 \]

5. **Final Result**:
The acceleration produced is:
\[ \mathbf{a} = 2 \hat{i} + 2 \hat{j} - 4 \hat{k} \, \text{m/s}^2 \]