In physics, the velocity of a particle,moving with constant acceleration a, with respect to time t, is given by v(t) = v0 + a(t t0), where v0 and t0 are the initial velocity and time of the particle, respectively.

Consider an object is travelling with a constant acceleration of 2m/s2, whose initial velocity is 1m/s and initial time is 3s.

a) Find the velocity function in the form v(t) = at + b.

b) Sketch the graph of v(t).