A variable force F = (3 x^2 + 2 x) i N acts on a 2 kg body causing it to move from x = 1 m to x = 3 m. What is the total work done by the force?

Answer and explanation

Correct answer: D. 34 J

  1. Step 1: Work W = ∫_(x1 to x2) F dx.
  2. Step 2: W = ∫_(1 to 3) (3x^2 + 2x) dx = [x^3 + x^2]_(1 to 3).
  3. Step 3: At x = 3: 3^3 + 3^2 = 27 + 9 = 36.
  4. Step 4: At x = 1: 1^3 + 1^2 = 1 + 1 = 2.
  5. Step 5: W = 36 - 2 = 34 J.

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