To find the required increase in the acting force, we use the formula: S = V ^ 2 / 2a = V ^ 2 / (2F / m); the resulting equality: Vk ^ 2 / (2Fk / m) = Vn ^ 2 / (2Fn / m); Vk ^ 2 / Fk = Vn ^ 2 / Fn, whence we express: Fk = Vk ^ 2 * Fn / Vn ^ 2.
The ratio of the variables: Vk (required speed) = 2Vn (initial speed).
Calculation: Fk = Vk ^ 2 * Fn / Vn ^ 2 = (2Vn) ^ 2 * Fn / Vn ^ 2 = 4Fn.
Answer: The effective force needs to be increased by 4 times.
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