The integral of acceleration yields velocity, which we are trying to find. So int(a(t)) = (t^2)/2 - cos(t) + C. So we can also say that v(t) = (t^2)/2 - cos(t) + C. *The constant, C, is very important in this case. We need to find when v(t) = 0. We can not do that without first knowing C. 2. Solve for C. -2 = v(0). -2 = (t^2)/2 - cos(t) + C. -2 = -cos(t) + C. -2 = -1 + C -1 = C.
Now we have the full velocity equation. v(t) = (t^2)/2 - cos(t) - 1. 4. Solve for t when velocity is 0. 0 = (t^2)/2 - cos(t) - 1. t = 1.478 or -1.478 *time cannot be negative, so answer is b.1.48
