A particle is moving along the x-axis whose acceleration is given by ` a= 3x-4`, where x is the location of the particle. At t = 0, the particle is at rest at `x = 4//3m`. The distance travelled by the particles in 5 s is

Options

A. zero
B. 42 m
C. Infinite
D. None of these

Explanation

To solve the problem, we need to analyze the motion of the particle given its acceleration function and initial conditions.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- The acceleration of the particle is given by the equation \( a = 3x - 4 \).
- At time \( t = 0 \), the particle is at rest at position \( x = \frac{4}{3} \) m.
- Since the particle is at rest, its initial velocity \( v_0 = 0 \).

2. **Calculating Initial Acceleration**:
- To find the initial acceleration, we substitute the initial position into the acceleration equation:
\[ a(0) = 3 \left(\frac{4}{3}\right) - 4 \]
- Simplifying this:
\[ a(0) = 4 - 4 = 0 \]
- Therefore, the initial acceleration \( a(0) = 0 \).

3. **Interpreting the Results**:
- Since the particle is at rest and has zero acceleration at \( t = 0 \), it suggests that there is no net force acting on the particle.
- According to Newton's first law, an object at rest will remain at rest unless acted upon by a net external force.

4. **Conclusion on Motion**:
- Given that both the initial velocity and acceleration are zero, the particle will not start moving.
- Thus, the distance traveled by the particle in any time interval, including 5 seconds, is zero.

5. **Final Answer**:
- The distance traveled by the particle in 5 seconds is \( 0 \) meters.