Final answer:
The displacement of the cyclist after riding 3 km west and then 2 km east is 1 km west, the distance traveled is 5 km, and the magnitude of displacement is 1 km.
Step-by-step explanation:
The displacement of a cyclist who rides 3 km west and then 2 km east is the difference between the two distances in a straight line and in a specified direction. To calculate the displacement, we subtract the eastward distance from the westward distance.
(a) The rider's displacement is: 3 km (west) - 2 km (east) = 1 km (west). Therefore, the displacement is 1 km west.
(b) The distance traveled is the total length of the path the cyclist has taken, which is the sum of the two distances: 3 km + 2 km = 5 km.
(c) The magnitude of displacement is the absolute value of the displacement, which is simply 1 km, regardless of direction.
The correct choice for the cyclist's displacement is therefore (b) 1 km west.