A swimmer is swimming to the left with a speed of 1.0 m/s when she starts to speed up with constant acceleration. The swimmer reaches a final speed of 2.5 m/s over a distance of 5.0 m. How long did the swimmer take to speed up to 2.5 m/s? Around the answer to two significant digits.

Correct answer: t = 2.86 seconds

Explanation:

We first use this formula

V² - V₀² = 2 a d

where V is the final velocity (speed), V₀ the initial velocity (speed),

a the acceleration and d the distance.

We will calculate the acceleration from this formula

a = (V² - V₀²) / (2 d) = (2.5² - 1²) / (2 · 5) = (6.25 - 1) / 10 = 5.25 / 10

a = 0.525 m/s²

then we use this formula

V = V₀ + a t = > t = (V - V₀) / a = (2.5 - 1) / 0.525 = 1.5 / 0.525 = 2.86 seconds

t = 2.86 seconds

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