A runner of mass 61.3 kg starts from rest and accelerates with a constant acceleration of 1.07 m/s² until she reaches a velocity of 8.1 m/s.She then continues running with this constant velocity.How far has she run (in meters)after 49.1 seconds? A)195.88 B)229.18 C)268.14 D)313.72 E)367.05

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Quizplus · Accepted Answer

The runner accelerates to 8.1 m/s with a constant acceleration of 1.07 m/s². First, calculate the time taken to reach this velocity using v = u + at, which gives t = 8.1 / 1.07 ≈ 7.57 seconds. The distance covered during acceleration is s = ut + 0.5at² = 0 + 0.5 * 1.07 * (7.57)² ≈ 30.77 meters. The remaining time is 49.1 - 7.57 = 41.53 seconds, during which she runs at 8.1 m/s. The distance covered at constant velocity is 8.1 * 41.53 ≈ 336.28 meters. Total distance = 30.77 + 336.28 = 367.05 meters.

A Runner of Mass 61