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A particle of mass 𝑚 is moving in the 𝑥𝑦-plane such that its velocity at a point (𝑥, 𝑦) is given as
v⃗ = 𝛼(𝑦𝑥̂ + 2𝑥𝑦̂), where 𝛼 is a non-zero constant. What is the force 𝐹 acting on the particle?
(A) 𝐹 = 2𝑚𝛼2(𝑥𝑥̂ + 𝑦𝑦̂ ) (B) 𝐹 = 𝑚𝛼2(𝑦𝑥̂ + 2𝑥𝑦̂ )
(C) 𝐹 = 2𝑚𝛼2(𝑦𝑥̂ + 𝑥𝑦̂ ) (D) 𝐹 = 𝑚𝛼2(𝑥𝑥̂ + 2𝑦𝑦̂ )
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