A 4.0-Kg particle is moving with a velocity 20.0 m/s in the +xdirection when it

Question

A 4.0-Kg particle is moving with a velocity 20.0 m/s in the +xdirection when it is at position x=1.0 For x>1.0 m, the particleexperiences a single force F= (-x)i, where =36.0N and =52.0 N/m. Determine (A) the work done by the force on the particle as it movesfrom x=1.0m to x=5.0m. (B) the velocity of the particle at x=5.0 m. (C) the position along the +x axis where the velocity of theparticle equals zero. A 4.0-Kg particle is moving with a velocity 20.0 m/s in the +xdirection when it is at position x=1.0 For x>1.0 m, the particleexperiences a single force F= (-x)i, where =36.0N and =52.0 N/m. Determine (A) the work done by the force on the particle as it movesfrom x=1.0m to x=5.0m. (B) the velocity of the particle at x=5.0 m. (C) the position along the +x axis where the velocity of theparticle equals zero.

Explanation / Answer

Given that         F = [ -x ] i            = [ 36.0 - 52.0 x ] i (a) Workdone = integral [ F.ds] = 4 -12 = 4 * 36 - 12 * 52 = - 480 J (b) a = [ - x ] i / m        dv / dt = [ -x ] i / m        dv = [ - x] i dt / m integrating both sides we get          v = [ 36 -52x ] i t / 4 at x = 5 , we have v = - 56t i (c) v = - 56t i      ==> dx / dt = - 56t i      ==> x = - 28t2

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