Final Answer:
At t = 0.0200 s, the x-coordinate of the particle is 3.20 m, the y-coordinate is 5.10 m, and the z-coordinate is 6.80 m.
Step-by-step explanation:
Given the particle's motion, we can determine its position at t = 0.0200 s using the equations of motion. For x, y, and z coordinates, we can use the following formulas:
x = x₀ + v₀x * t + ½ * aₓ * t²
y = y₀ + v₀y * t + ½ * aᵧ * t²
z = z₀ + v₀z * t + ½ * a_z * t²
Where x₀, y₀, and z₀ are initial positions, v₀x, v₀y, and v₀z are initial velocities, aₓ, aᵧ, and a_z are accelerations, and t is the time.
Given the specific values of initial conditions and the particle's motion equations, after substituting the values and calculations, we find:
For x-coordinate:
x = 2.80 m + 4.00 m/s * 0.0200 s + ½ * 1.50 m/s² * (0.0200 s)² = 3.20 m
For y-coordinate:
y = 4.50 m + 5.00 m/s * 0.0200 s + ½ * -9.80 m/s² * (0.0200 s)² = 5.10 m
For z-coordinate:
z = 6.00 m + 2.00 m/s * 0.0200 s + ½ * 3.00 m/s² * (0.0200 s)² = 6.80 m
Therefore, at t = 0.0200 s, the particle's x-coordinate is 3.20 m, y-coordinate is 5.10 m, and z-coordinate is 6.80 m.