A

Given:
The position of the particle is defined by:

• x = t
• y = 3t - 5

(i) Path Traced by the Particle:
To find the path traced by the particle, we can express y in terms of x. Since x = t, we can substitute this into the equation for y:

• y = 3(t) - 5
• y = 3x - 5

This represents the equation of a straight line with a slope of 3 and a y-intercept of -5.

(ii) When does the particle cross the X-axis?
A particle crosses the X-axis when y = 0. Setting the equation for y to zero:

• 0 = 3t - 5
• 3t = 5
• t = \frac{5}{3}

Thus, the particle crosses the X-axis at time t = \frac{5}{3}.
Therefore, the path traced is a straight line, and it crosses the X-axis at t = \frac{5}{3}.