A particle moves 5m in the +x direction while being acted upon by a constant force`vecF = (4 N)hati + (2N)hatj - (4N)hatk` . The work done on the particle by this force is

Options

A. (a)20 J
B. (b)10 J
C. (c)`-20 J`
D. (d)30 J

Explanation

To find the work done on the particle by the given force, we can follow these steps:

### Step 1: Identify the Force and Displacement
The force acting on the particle is given as:
\[ \vec{F} = 4 \hat{i} + 2 \hat{j} - 4 \hat{k} \, \text{N} \]
The displacement of the particle is 5 m in the +x direction, which can be represented as:
\[ \vec{d} = 5 \hat{i} + 0 \hat{j} + 0 \hat{k} \, \text{m} \]

### Step 2: Calculate the Work Done
The work done \( W \) by a force is calculated using the dot product of the force vector and the displacement vector:
\[ W = \vec{F} \cdot \vec{d} \]
Calculating the dot product:
\[ W = (4 \hat{i} + 2 \hat{j} - 4 \hat{k}) \cdot (5 \hat{i} + 0 \hat{j} + 0 \hat{k}) \]
This expands to:
\[ W = (4 \cdot 5) + (2 \cdot 0) + (-4 \cdot 0) \]
\[ W = 20 + 0 + 0 = 20 \, \text{J} \]

### Step 3: Conclusion
The work done on the particle by the force is:
\[ \boxed{20 \, \text{J}} \]

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