Keeping in mind that:
- Distance is the length of the total path covered by the person, regardless of the directions of the different parts of motion
- Displacement is just the distance in a straight line between the final point and the initial point
Let's apply these concepts to solve the different parts of the problem:
1. 120 m, 80 m west
The total distance is the sum of the length of the different paths:
distance = 100 + 20 = 120 m
To find the displacement, we need to find the distance between the starting point and the ending point. Assuming the starting point as
x = 0
Michelle moved 100 m westward and 20 m eastward, so the ending point is at
ending point = 100 - 20 = 80 m (westward)
So, the displacement is
displacement = 80 - 0 = 80 m (west)
2. 6400 m, 0
The distance is equal to the length of the track multiplied by the number of laps, so:
The track is circular, and the runner completes exactly 4 laps: it means that at the end of the motion, the runner is at her starting point. So ending point and starting point coincide, and so the displacement
displacement = ending point - starting point = 0
3. 40 m; 10 m forward
The total distance is just the sum of the lengths of the different parts of the motion, so:
distance = 20 + 5 + 10 + 5 = 40 m
The find the displacement, we need to assign signs to every direction:
Forward --> positive along the forward-backward direction
Backard --> negative along the forward-backward direction
Right --> positive direction along the right-left direction
Left --> negative direction along the right-left direction
Along the forward-backward direction, the displacement is:
20 m forward and 10 m backward, so 20 - 10 = 10 (forward)
Along the left right direction, the displacement is:
5 m right and 5 m left, so 5 - 5 = 0
So the net displacement is 10 m (forward)
4. 16 km; 4 km south
Again, t total distance is the sum of the lengths of the different parts of the motion, so:
distance = 2 + 4 + 6 + 4 = 16 km
To find the displacement, we assign signs to every direction:
North --> positive along the north-south direction
south --> negative along the north-south direction
east --> positive direction along the east-west direction
west --> negative direction along the east-west direction
Along the north-south direction, the displacement is:
2 km north and 6 km south, so 2 - 6 = -4 km (4 km south)
Along the east-west direction, the displacement is:
4 km east and 4 km west, so 4 - 4 = 0
So the net displacement is 4 km south
5. 37.7 m; 24 m
The distance covered by the skater is the length of half circumference, so given the radius
r = 12 m
The distance is
The displacement is the distance in a straight line between the ending position and the starting position. Since the skater ends her motion halfway around the circle, the distance between the initial and final point is equal to the diameter of the circle (two times the radius). So,