Find the velocity vector and position vectors?

Question

Given an acceleration vector, initial velocity (u₀, v₀), and initial position (x₀, y₀), find the velocity and position vector for t >= 0.

a(t)=<cos(t), 5sin(t)>

<u₀, v₀> = <0, 2>

<x₀, y₀> = <2, 0>

Answer 1

v(t) = ∫a(t)dt

s(t) = ∫v(t)dt

v(t) = ∫<cos(t), 5sin(t)> dt = <sin(t), -5cos(t) + 2>

s(t) = ∫<sin(t), -5cos(t)+2>dt = <-cos(t) + 2, -5sin(t) + 2t>