After the person walked 8.00 km west, then went 3.00 km east and then went back 1.00 km west, we have:
a) The person's distance is 12.00 km.
b) The person's displacement is 6.00 km west.
a) The total distance is a scalar that is given by the sum of the three short distances traveled by the person:
[tex] d = d_{1} + d_{2} + d_{3} [/tex]
Where:
d₁ = 8.00 km
d₂ = 3.00 km
d₃ = 1.00 km
The total distance is:
[tex] d = d_{1} + d_{2} + d_{3} = 8.00 km + 3.00 km + 1 km = 12.00 km [/tex]
Hence, the person's distance is 12.00 km.
b) The displacement is a vector that is given by the sum of the directions of the distances:
[tex] \Delta x = x_{1} + x_{2} + x_{3} [/tex]
Where:
x₁ = 8.00 km
x₂ = -3.00 km
x₃ = 1.00 km
The minus sign of x₂ is because we are taking the west direction as the positive x-direction.
The displacement is:
[tex] \Delta x = 8.00 km - 3.00 km + 1.00 km = 6.00 km [/tex]
Therefore, the person's displacement is 6.00 km west.
To learn more about distance and displacement go here: https://brainly.com/question/14054120?referrer=searchResults
I hope it helps you!
