A bicyclist, initially at rest, begins pedaling and gaining speed steadily for 4.90s during which she covers 25.0m. What was her final speed (in given units)?
mph

The bicyclist accelerates with magnitude a such that

25.0 m = 1/2 a (4.90 s)²

Solve for a :

a = (25.0 m) / (1/2 (4.90 s)²) ≈ 2.08 m/s²

Then her final speed is v such that

v ² - 0² = 2a (25.0 m)

Solve for v :

v = √(2 (2.08 m/s²) / (25.0 m)) ≈ 10.2 m/s

Convert to mph. If you know that 1 m ≈ 3.28 ft, then

(10.2 m/s) • (3.28 ft/m) • (1/5280 mi/ft) • (3600 s/h) ≈ 22.8 mi/h

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