Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = cos(t) - sin(t) and v(0) = 3

Question

v(t) = sin(t) + cos(t) + 3
v(t) = sin(t) + cos(t) + 2
v(t) = sin(t) - cos(t) + 3
v(t) = sin(t) - cos(t) + 4

Answer 1

v(t) = ∫ a(t) dt
= ∫ cost-sint dt
= sint+cost+C
Now plug in (0,3) to find C