Question

An object with an initial position of x(0) = 3 has a velocity of v(t) =sin(t). Find its position at t =2.

Answer 1

x(t) = -cos t + c
now you know that x(0) = 3, so plug in t=0 to find c.

Then you can use t=2 to get x(2)

Answer 2

So the answer would be -cos(2)+4=4.416?

Answer 3

Looks good to me.