A swimmer completes two lengths of a 50 m pool. The table shows her times. Length Distance / m Time / s 1st (outward) 50 32 2nd (return) 50 38 What are the ...
Question 1 Report
A swimmer completes two lengths of a 50 m pool. The table shows her times.
| Length | Distance / m | Time / s |
|---|---|---|
| 1st (outward) | 50 | 32 |
| 2nd (return) | 50 | 38 |
What are the average speed and the average velocity for the whole swim?
Answer Details
Average speed uses the total distance swum, while average velocity uses the net displacement from start to finish. The swimmer covers 50 m out and 50 m back, a total distance of 100 m, in a total time of \(32+38=70\ \text{s}\):
\[ \overline{v}_{speed} = \frac{100}{70} = 1.43\ \text{m/s} \]but since she finishes exactly back where she started (at the same end of the pool), her net displacement is zero, so
\[ \overline{v}_{velocity} = \frac{0}{70} = 0\ \text{m/s} \]A common mistake is quoting the same non-zero value for both quantities, forgetting that velocity is a vector and the outward and return displacements exactly cancel over a there-and-back journey, while speed (a scalar) does not.
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