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Andrea, a 61.5 kg sprinter, starts a race with an acceleration of 3.700 m/s2. If she accelerates at that rate for 12.00 m and then maintains that velocity for the remainder of a 100.00 m dash, what will her time (in s) be for the race

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Answer:

The total time it will take her to complete the race is 13.17 s

Explanation:

Given;

mass of the sprinter, m = 61.5 kg

acceleration of the sprinter, a = 3.7 m/s²

first distance covered, d₁ = 12 m

Determine her velocity for the first 12 m;

v² = u²  + 2as

v² = 0  +  (2 x 3.7 x 12)

v² = 88.8

v = √88.8

v = 9.42 m/s

Determine her time for the first 12 m;

v = u + at

9.42 = 0 + 3.7t₁

9.42 = 3.7t₁

t₁ = 9.42 / 3.7

t₁ = 2.55 s

Determine the time it will take her to complete the last 100 m at a constant velocity of 9.42 m/s

s = vt₂ + ¹/₂at₂²

s = vt₂ + ¹/₂(0)t₂²

s = vt₂

100 = 9.42t₂

t₂ = 100 / 9.42

t₂ = 10.62 s

The total time it will take her to complete the race = 2.55 s + 10.62 s

                                                                                    = 13.17 s

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