A particle of mass 2 kg moves along the x-axis under a…
Question
A particle of mass 2 kg moves along the x-axis under a position-dependent net force F(x) = (6x - 3x^2) N, where x is in metres. The particle starts from rest at x = 0 and moves in the +x direction. Find the maximum speed (in m/s) the particle attains during its subsequent motion.
Step-by-step solution
The speed is maximum where acceleration (hence net force) is zero: 6x - 3x^2 = 0 => x(2 - x)*3 = 0 => x = 2 (the first positive zero, where the particle is still speeding up).
Kinetic energy gained equals the work done: W = integral_0^2 (6x - 3x^2) dx = [3x^2 - x^3]_0^2 = 12 - 8 = 4 J.
Final answer2
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