A particle of unit mass moves in a straight line against a resistance numerically
equal to v + v^3, where v is its velocity.Initially the particle is at the origin and is
travelling with velocity Q, where Q>0.
(a) Show that v is related to the displacement x by the formula x = arctan[(Q−v)/(1+Qv)].
(b) Show that the time t which has elapsed when the particle is travelling with velocity v is given by t = 1/2ln([Q^2 (1+v^2)]/[v^2(1+Q^2)]
(c) Find v^2 as a function of t.
(d) Find the limiting values of v and x as t → ∞
Is someone able to work this through and post the worked answers?
equal to v + v^3, where v is its velocity.Initially the particle is at the origin and is
travelling with velocity Q, where Q>0.
(a) Show that v is related to the displacement x by the formula x = arctan[(Q−v)/(1+Qv)].
(b) Show that the time t which has elapsed when the particle is travelling with velocity v is given by t = 1/2ln([Q^2 (1+v^2)]/[v^2(1+Q^2)]
(c) Find v^2 as a function of t.
(d) Find the limiting values of v and x as t → ∞
Is someone able to work this through and post the worked answers?
