1. Suppose an object has acceleration given by a(t) = et,cos(t),1 m/s2, with initial

velocity 3sqrt(2) m/s in the direction of i + j, and initial position 12 m from the origin (in

the y-direction).

(a) Find a function that models the velocity of the object and another that models the position of the object at time t.

Hint: These should be vector-valued functions. Include units in your answer.