Question

A particle moves along a line so that at any time t ≥ 0 its velocity is given by v(t) = t/(1+t^2). At time t = 0 the position of the particle is s(0) = 5.

a) Determine the max velocity of this particle. Justify.
b) Determine the position of the particle at t = 3.
c) Find the limiting value of the velocity as t increases without bound.