Question

Dear Sir,
I do need help. Please answer the following question.

A particle moves in a straight line along the X-axis, with an initial velocity of and an initial position of x0. The acceleration of the particle is proportional to the velocity, and the proportional coefficient is k, which is opposite to the velocity. Please determine (1) ; (2) x(t).

Thanks

Answer 1

5019 Given, quitial conda lie at t=o) VLE) = Vo and xitl=de and also given, => ( As accelaration is properst- ional to velocity and -ve sign accelaration is opposite to velocity) is due to So, ac : -KUCH) du It = -KU du a-kat * Integrate Both side eur=-kt tene, => eu (u) = okt -Kt ucti= cekt -e At t=0, V(t) = V. so, C-V. VCt)veke . 7 da dt = vekt →dx= vekt at set=_VO (integrate Both side) -kt K +2 At t=0, It's to So, sho - u sta => ₂ = not s gold :: a(t) = - u ha ett + +do + vo xt u :(1-2). txo