example that show the # part of distance and the # part of displacement can be different for the same motion
if you make a round trip somewhere, returning to the same place where you started, the distance travelled is some number of kilometers travelled, but the displacement is zero.
Sure, here's an example that demonstrates how the magnitude of distance and displacement can differ for the same motion.
Suppose a person takes a walk around their neighborhood, starting at their front door and ending back at their front door. During the walk, they make several stops along the way to chat with neighbors. Here are the specific distances covered during each leg of the journey:
- Leg 1: The person walks 100 meters from their front door to the first neighbor's house.
- Leg 2: After chatting with the first neighbor, they walk 200 meters to the second neighbor's house.
- Leg 3: After chatting with the second neighbor, they walk 150 meters to the third neighbor's house.
- Leg 4: After chatting with the third neighbor, they walk 250 meters back to their front door.
To calculate the total distance covered during the walk, we add up the distances covered during each leg:
Total distance = 100 meters + 200 meters + 150 meters + 250 meters = 700 meters
The total distance covered is 700 meters.
Now let's consider the displacement, which refers to the straight-line distance and direction between the initial and final positions.
In this example, the person starts and ends at their front door, meaning the initial and final positions are the same. Therefore, the displacement is the straight-line distance from the front door to the front door, which is zero.
Displacement = 0 meters
Here, we can observe that the magnitude of the distance covered (700 meters) is different from the magnitude of the displacement (0 meters). The person walked a total distance of 700 meters, but the displacement is zero as they returned to their starting point.
This example highlights how distance and displacement can differ for the same motion, especially when considering changes in direction or when returning to the initial position.
Sure! Let's consider a scenario where an object moves in a straight line.
Suppose the object starts at point A, moves 5 meters to the right to reach point B, and then returns back to point A by moving 5 meters to the left.
In this case, the distance traveled by the object is equal to the total path length covered. The object moves 5 meters to the right and then 5 meters back to the left, resulting in a total distance of 10 meters.
However, the displacement of an object captures only the change in position from the starting point to the ending point. In this scenario, the object starts and finishes at the same point, so the displacement is zero. Displacement is a vector quantity and is defined by both magnitude and direction. In this case, the magnitude of the displacement is 0 meters since there is no overall change in position.
So, in this example, the distance traveled is 10 meters, while the displacement is 0 meters. The distance takes into account the entire path followed by the object, while the displacement considers only the change in position.