A particle with mass m moves in the xy-plane, where its velocity at the coordinates (x, y) is described by v = α(yx̂ + 2xŷ), with α being a constant that is not zero. What is the force F experienced by the particle?

F = 2mα²(yx̂ + xŷ)
F = mα²(yx̂ + 2xŷ)
F = 2mα²(yx̂ + xŷ)
F = mα²(yx̂ + 2xŷ)

Correct answer: F = 2mα²(yx̂ + xŷ)

Solution

The velocity is given as a function of position, and the force is derived using Newton's second law, F = m(dv/dt). Substituting the velocity expression and differentiating, the force is found to be 2mα²(yx̂ + xŷ).

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