Final answer:
To find the position of the particle, we integrate the given velocity function using integration techniques. The constant of integration is determined by substituting the initial time value into the position function. The position function is s(t) = -cos(t) - sin(t) + 7.
Step-by-step explanation:
To find the position of the particle, we will integrate the velocity function. Given v(t) = sin(t) - Cos(t), we can integrate it with respect to time to get the position function.
The integral of sin(t) is -cos(t) and the integral of cos(t) is sin(t). So the position function will be -cos(t) - sin(t) + C, where C is the constant of integration.
Since we are given that s(0) = 6, we can substitute t = 0 into the position function and solve for C. Plugging in t = 0, we get -cos(0) - sin(0) + C = 6. Simplifying, we find that C = 6 + 1 = 7.
Therefore, the position function of the particle is s(t) = -cos(t) - sin(t) + 7.