Example from Physics, 2.1 Relative Motion, Distance, and Displacement

Calculating Distance and Displacement

A cyclist rides 3 km west and then turns around and rides 2 km east. (a) What is her displacement? (b) What distance does she ride? (c) What is the magnitude of her displacement?

A segment is shown, divided into two sections. The first section is labeled change in d two equals plus twelve kilometers and has a right pointing arrow, ending at a label df. The second section is labeled do at the end of it. A left-pointing arrow is above the entire segment and is labeled change in d one equals negative three kilometers. The right of the segment, a left-pointing arrow is shown with a W and a negative sign on the left side and E and a positive sign on the right side. The label do is in the center.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
To solve this problem, we need to find the difference between the final position and the initial position while taking care to note the direction on the axis. The final position is the sum of the two displacements, $Δ d_{1}$ and $Δ d_{2}$ .
2
Solution
1. Displacement: The rider’s displacement is $Δ d = d_{f} - d_{0} = - 1 km$ .
2. Distance: The distance traveled is 3 km + 2 km = 5 km.
3. The magnitude of the displacement is 1 km.

0 of 2 steps open

How did it go?

Strategy

Solution

Strategy

Solution