A particle is travelling along X-axis and its x-coordinate is related to time as follows:
`x=5t^(2)-20`
Here x is measured in metres and time t in seconds.
When does the particle reverse its direction of motion?

Options

A. 2s
B. 3s
C. 1s
D. never

Explanation

To determine when the particle reverses its direction of motion, we need to analyze the given position function and find the velocity.

### Step-by-Step Solution:

1. **Given Position Function**: The position of the particle is given by the equation:
\[ x(t) = 5t^2 - 20 \]
where \(x\) is in meters and \(t\) is in seconds.

2. **Find the Velocity**: The velocity \(v(t)\) of the particle is the derivative of the position function with respect to time \(t\). We can find it using the formula:
\[ v(t) = \frac{dx}{dt} \]
Differentiating the position function:
\[ v(t) = \frac{d}{dt}(5t^2 - 20) = 10t \]

3. **Analyze the Velocity**: The velocity function we obtained is:
\[ v(t) = 10t \]
This indicates that the velocity is directly proportional to time \(t\).

4. **Determine When the Particle Reverses Direction**: A particle reverses its direction of motion when its velocity changes sign (from positive to negative or vice versa). Since \(v(t) = 10t\):
- For \(t < 0\), \(v(t)\) is negative (not applicable here since \(t\) cannot be negative).
- For \(t = 0\), \(v(0) = 10 \times 0 = 0\).
- For \(t > 0\), \(v(t)\) is positive.

Therefore, the velocity is zero only at \(t = 0\) and positive for all \(t > 0\).

5. **Conclusion**: Since the velocity does not become negative for any \(t \geq 0\), the particle does not reverse its direction of motion. Thus, the answer is that the particle never reverses its direction.

### Final Answer:
The particle never reverses its direction of motion.