Question

1. a dog moves from point a to point b to point c, then back to point b along the line shown in the figure below.

what is the dogs distance and displacement?

Explanation:

Step1: Calculate the distance

Distance is the total path length.
The dog moves from \(A(0)\) to \(B(6)\): \(d_1=|6 - 0|=6\) meters.
Then from \(B(6)\) to \(C(11)\): \(d_2=|11 - 6| = 5\) meters.
Then from \(C(11)\) back to \(B(6)\): \(d_3=|6 - 11|=5\) meters.
Total distance \(d=d_1 + d_2 + d_3=6+5 + 5=16\) meters.

Step2: Calculate the displacement

Displacement is the change in position from the initial to the final point.
Initial position \(x_i=0\) (point \(A\)), final position \(x_f = 6\) (point \(B\)).
Displacement \(\Delta x=x_f-x_i=6 - 0=6\) meters (towards East as per the coordinate system).

Answer:

Distance: \(16\) meters; Displacement: \(6\) meters East.