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A body of mass 1 kg, initially at rest on a smooth horizontal…
Question
A body of mass 1 kg, initially at rest on a smooth horizontal surface, is acted upon by a net horizontal force that varies with position as F = 3x^2 newtons, where x is in metres measured along the direction of motion. Find the speed (in m/s) of the body after it has moved 2 m from rest.
✓ Verified answer: 4checked by our engine — not a guess
Step-by-step solution
Work done by the variable force from x = 0 to 2 m: W = integral of 3x^2 dx = [x^3] from 0 to 2 = 8 J.
By the work-energy theorem, (1/2)(1)v^2 = 8, so v^2 = 16 and v = 4 m/s.
Final answer4
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