Question

PROBLEM 2 (10 POINTS) A particle of mass m moving along a straight line is acted on by a retarding force (one directed against the motion) F = beau, where b and a are constants and u is the velocity. At に0, it is moving with velocity 10. Find the velocity at later times always

Answer 1

Because F = -be^av --(1) because F = MA = m dv/dt ---(2) implies m dv/dt = -b e^av implies dv/dt = (-b/m) e^av implies dv/e^av = (-b/m) dt implies integral_v_0^v e^-av dv = integral_0^t (-b/m) dt implies [e^-av/-a]_v_0^v = (-b/m) t implies e^-av - e^-av_0 = ab/m times t implies e^-av = e^-av_0 + ab/m times t implies -av = ln (ab/m + e^-av_0) implies V = 1/a [ln (ab/m t + e^-av_0)]