Describing Motion

Displacement is the straight-line distance from the starting point to the finishing point, including direction. It is a vector quantity that depends only on start and end positions, not the path taken.

The swimmer starts at one end of the pool. After two full laps (50 m down and 50 m back), they are back at the exact same position where they started.

Since the start and end positions are the same, the straight-line distance between them is zero. Therefore, displacement = 0 m.

Note that the distance travelled is $50+50=100$ m, but this is different from displacement. Displacement = 0 m.

The question asks for displacement (not distance). Displacement is a vector quantity measuring the straight-line distance from start to end position.

200 m would require the swimmer to end up 200 m away from the start. This is impossible in a 50 m pool. Eliminate.

100 m is the total distance travelled ($50+50$ m), but distance and displacement are different quantities. After two laps the swimmer is not 100 m away from the start. Eliminate.

50 m would be the displacement after only one lap (finishing at the far end). After two full laps the swimmer returns to the start. Eliminate.

0 m is correct because the swimmer ends at the same position they started. The straight-line distance from start to finish is zero, so displacement = 0 m.

We need to convert km/h to m/s. The conversion rule is: divide by 3.6. This comes from the fact that $1\text{ km/h}=\frac{1000\text{ m}}{3600\text{ s}}=\frac{1}{3.6}\text{ m/s}$.

$90\text{ km/h}÷3.6=25\text{ m/s}$

The car's speed is 25 m/s. This is a very useful benchmark to remember — 90 km/h = 25 m/s.

Converting km/h to m/s means the number should get smaller (metres per second are smaller intervals than kilometres per hour). We expect a result less than 90.

90 m/s would mean no conversion was done. 324 m/s is larger than the original — this would happen if someone incorrectly multiplied by 3.6 instead of dividing. Both are wrong. Eliminate both.

32.4 m/s results from dividing by 2.78 instead of 3.6, or from an incorrect conversion. The correct conversion is $90÷3.6$, not $90÷2.78$. Eliminate.

25 m/s is correct: $90÷3.6=25$ m/s. This is the proper km/h to m/s conversion.