A particle moves in the xy-plane from the origin to the point (5, 5) along a straight line. It experiences a force F = (2y i-hat + x² j-hat) N, where x and y are in metres. Calculate the work done by the force on the particle.

125 J
66.7 J
35 J
25 J

Correct answer: 66.7 J

Solution

Parametrizing the straight path as x = t, y = t (t: 0 to 5): W = integral₀⁵ (2t + t²) dt = [t² + t³/3]₀⁵ = 25 + 125/3 = 25 + 41.67 = 66.67 J approx 66.7 J.

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