Final answer:
The distance formula, √[(x2 - x1)^2 + (y2 - y1)^2], calculates the linear distance between two points, while the midpoint formula, [(x1 + x2)/2, (y2 + y1)/2], finds the midpoint. Displacement is the straight-line path with direction from start to end point, and distance traveled is the total path length covered.
Step-by-step explanation:
The distance formula is used to calculate the distance between two points in a coordinate system, derived from the Pythagorean theorem. The formula is √[(x2 - x1)^2 + (y2 - y1)^2], where (x1, y1) and (x2, y2) are the coordinates of the two points. Meanwhile, the midpoint formula is used to find the point that is exactly halfway between two given points, given by [(x1 + x2)/2, (y2 + y1)/2].
In physics, displacement is a vector quantity that refers to the change in position of an object. It is the straight-line path between the starting point and the ending point. Distance traveled, on the other hand, is a scalar quantity that refers to the total length of the path an object has moved, regardless of the direction.
To address the given questions:
- The total distance traveled is the sum of the distances over the entire path an object has moved.
- Displacement is the straight-line distance between the starting point and the ending point, along with the direction.
- You would want to use the distance when you need to know how much ground has been covered, and displacement when you are interested in knowing the shortest path between two points and the direction of that path.