Please include each step in solving the following problems:
1.) A particle starts moving with the initial velocity v(0) = 1 and accelerates as a(t) = sin t + t for t > 0.
(a) Find the velocity function for the particle.
(b) What would be its velocity at time t = 5.
2.) An object starts from rest and has an acceleration of a(t) = t^2 .
(a) What is its velocity after 3 seconds?
(b) What is its position after 3 seconds?