Answer
(a) $distance~traveled=14~m$
$displacement=\Delta x=2\times4.5~m=9.0~m$
(b) The distance traveled increases.
(c) The displacement decreases.
(d) $distance~traveled=28~m$.
$displacement=0$.
Work Step by Step
Let C be the perimeter of the circular track of radius r. Then
$C=2πr$
(a) The distance traveled is half of the perimeter. $r=4.5~m$:
$distance~traveled=\frac{C}{2}=πr=4.5π~m=14~m$
The displacement is the length of the segment joining the final position and the initial position. In this case, the diameter = 2r.
$displacement=\Delta x=2\times4.5~m=9.0~m$
(b) When the child completes one circuit, the distance traveled is equal to the perimeter of the circular track, but $C\gt\frac{C}{2}$
The distance traveled always increase.
(c) When the child completes one circuit, the initial position and the final position are the same: $x_{i}=x_{f}$. The displacement is zero.
(d) $distance~traveled=C=2πr=2π\times4.5~m=28~m$
$displacement=\Delta x=x_{f}-x_{i}=0$
