Question

4 sep use mathematics a cyclist rides 3 km west and then turns around and rides 2 km east. what is her displacement? what total distance does she ride?

Explanation:

Step1: Define displacement and distance

Displacement is the straight - line distance from the initial position to the final position, considering direction. Let's take west as the positive direction for simplicity. The cyclist rides 3 km west (so displacement component \(d_1 = + 3\) km) and then 2 km east (displacement component \(d_2=- 2\) km, since east is opposite to west). Distance is the total length of the path traveled, regardless of direction.

Step2: Calculate displacement

To find the displacement \(D\), we sum up the individual displacement components. So \(D=d_1 + d_2\). Substituting the values, we get \(D = 3\space km-2\space km=1\space km\) west (since the result is positive, the direction is west).

Step3: Calculate distance

To find the total distance \(d\), we sum up the magnitudes of the individual paths. The first path is \(3\space km\) and the second path is \(2\space km\). So \(d = 3\space km + 2\space km=5\space km\).

Answer:

Displacement: \(1\space km\) west; Total distance: \(5\space km\)