Kinematics: Question 1

Worked solution

Step 1: Recall the difference between distance and displacement

Distance is a scalar quantity (it is the total length of the path travelled, regardless of direction. Displacement is a vector quantity) it is the straight-line distance from the starting point to the finishing point, together with a direction (or, as asked here, just its magnitude).

Step 2: Find the total distance travelled

The cyclist travels $300\text{ m}$ east, then $120\text{ m}$ west. Since distance ignores direction, these two path lengths simply add: $300\text{ m} + 120\text{ m} = 420\text{ m}$

Step 3: Find the magnitude of the displacement

Displacement depends only on the start and finish points. Taking east as positive, the cyclist’s net position change is: $(+300\text{ m}) + (-120\text{ m}) = +180\text{ m}$

So the magnitude of her displacement from the starting point is $180\text{ m}$ (in the eastward direction). Smaller than the total distance, because part of the $300\text{ m}$ eastward journey was “cancelled out” by riding back $120\text{ m}$ west.

Why the other options are wrong

• B: swaps the two values. $180\text{ m}$ is the displacement, not the distance, and $420\text{ m}$ is the distance, not the displacement.
• C: applies $420\text{ m}$ to both quantities, ignoring that the return leg reduces the net displacement below the total path length.
• D: applies $180\text{ m}$ to both quantities, incorrectly treating the total distance as if backtracking did not add extra path length.

Final answer

• Total distance $= \boxed{420}\text{ m}$, magnitude of displacement $= \boxed{180}\text{ m}$, option A.