Given data:
Acceleration (a) = 4 m/s²
Time (t) = 1.5 seconds

Using the equation of motion:
The displacement (s) of a particle can be calculated using the equation:
s = ut + (1/2)at²

Where:
s = displacement
u = initial velocity (which is 0 in this case)
t = time
a = acceleration

Calculating the displacement:
In order to find the displacement covered by the particle in the first half second, we need to consider the time interval from 0 to 0.5 seconds.

Using the equation of motion:
s = 0(0.5) + (1/2)(4)(0.5)²
s = 0 + (1/2)(4)(0.25)
s = 0 + (2)(0.25)
s = 0.5 meters

Therefore, the particle covers a displacement of 0.5 meters in the first half second.

Explanation:
The equation of motion relates the displacement of a particle with its initial velocity, time, and acceleration. In this case, the particle starts from rest, so its initial velocity (u) is 0 m/s. The given acceleration (a) is 4 m/s².

To find the displacement covered by the particle in a given time interval, we substitute the values of u, t, and a into the equation of motion and solve for s.

In the first half second (0 to 0.5 seconds), the particle has an acceleration of 4 m/s². Plugging in the values, we find that the displacement covered by the particle in this time interval is 0.5 meters.

This means that in the first half second, the particle moves 0.5 meters in the positive direction.

Conclusion:
The particle covers a displacement of 0.5 meters in the first half second.