To find the distance and displacement of the particle's motion, we can visualize the particle's path on a coordinate plane.
The particle initially moves 3 meters north, so we can mark a point 3 units above the origin (assuming the starting point is the origin). Then, it moves 4 meters east from that point, so we mark another point 4 units to the right of the previous point. Finally, it moves 6 meters south, so we mark a third point 6 units below the second point.
The path of the particle forms a right-angled triangle. We can use the Pythagorean theorem to find the distance and the straight-line displacement between the starting point and the final position.
Distance: The distance is the total length of the path traveled by the particle. In this case, it is the sum of the lengths of the three sides of the triangle formed by the particle's path. Using the Pythagorean theorem:
Distance = sqrt(3^2 + 4^2) + 6 = sqrt(9 + 16) + 6 = sqrt(25) + 6 = 5 + 6 = 11 meters
Therefore, the distance traveled by the particle is 11 meters.
Displacement: Displacement refers to the change in position of the particle from the starting point to the final position. To find the displacement, we can calculate the straight-line distance between the starting point and the final position of the particle.
Using the Pythagorean theorem again:
Displacement = sqrt(3^2 + (4-6)^2) = sqrt(9 + (-2)^2) = sqrt(9 + 4) = sqrt(13) meters
Therefore, the displacement of the particle is sqrt(13) meters (approximately 3.61 meters).