Final answer:
The distance covered by the object is 4 km. The magnitude of the displacement is √2 km and the direction is 45° counterclockwise from the positive x-axis.
Step-by-step explanation:
Let's analyze the path from point A to point B to point C and then back to point B and finally to point C. To find the distance covered by the moving object, we need to sum up the distances between each consecutive pair of points. From A to B, the object covers a distance of 1 km. From B to C, it covers another 1 km. Then, it travels back from C to B, covering 1 km again. Finally, it moves from B to C, covering 1 km. So, the total distance covered by the object is 1 + 1 + 1 + 1 = 4 km.
To find the magnitude and direction of the displacement, we only need to consider the starting and ending points. The object starts at A and ends at C. The displacement is the straight-line distance between these two points. To calculate this, we can use the Pythagorean theorem. Let's assume the distance from A to C is d. Using the theorem, we have:
d^2 = (1 km)^2 + (1 km)^2 = 2 km^2
d = √(2) = √2 km
Therefore, the magnitude of the displacement is √2 km. To find the direction, we can use trigonometry. Let's assume the angle between the displacement vector and the positive x-axis is θ. Since the displacement vector forms a right triangle with the x-axis, we can use the tangent function to find θ. Let's consider the side opposite to the angle (1 km) and the side adjacent to the angle (1 km). We have:
tan(θ) = opposite/adjacent = 1 km / 1 km = 1
θ = arctan(1) = 45°
Therefore, the displacement is √2 km along a direction 45° counterclockwise from the positive x-axis.