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 cross the origin?

Options

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

Explanation

To find out when the particle crosses the origin, we need to determine when its x-coordinate is equal to zero. The relationship given is:

\[ x = 5t^2 - 20 \]

### Step-by-Step Solution:

1. **Set the equation for x to zero**: Since we want to find out when the particle crosses the origin, we set \( x = 0 \).
\[ 0 = 5t^2 - 20 \]

2. **Rearrange the equation**: We can rearrange the equation to isolate the term involving \( t^2 \).
\[ 5t^2 = 20 \]

3. **Divide both sides by 5**: To solve for \( t^2 \), divide both sides of the equation by 5.
\[ t^2 = \frac{20}{5} = 4 \]

4. **Take the square root**: Now, we take the square root of both sides to solve for \( t \).
\[ t = \sqrt{4} = 2 \quad \text{or} \quad t = -\sqrt{4} = -2 \]

5. **Consider the physical context**: Since time cannot be negative in this context, we discard \( t = -2 \).
\[ t = 2 \text{ seconds} \]

### Final Answer:
The particle crosses the origin at \( t = 2 \) seconds.