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

Question

a) v(t)=sin(t) + cos(t) +3
b) v(t)=sin(t) + cos(t) +2
c) v(t)= sin(t) - cos(t) +3
d) v(t)= sin(t) - cos(t) +4

Answer 1

a = cost - sint = dv/dt
so, v = sint + cost + C
now solve v(0) = 3 to find C

Answer 2

so will be answer A, right?

Answer 3

NO!
sin(0) + cos(0) + C = 3