Find the position and velocity of an object moving along a straight line with the given acceleration, initial velocity, and initial position. \( a(t)=\cos \pi t, v(0)=7, s(0)=5 \) The velocity is \( v(t)=7+\frac{\sin (\pi t)}{\pi} \) (Type an exact answer.) The position is \( s(t)=\square \) (Type an exact answer.)

To find the position function \( s(t) \), we start with the known velocity function \( v(t) = 7 + \frac{\sin(\pi t)}{\pi} \). We can integrate the velocity function to obtain the position function: \[ s(t) = \int v(t) \, dt = \int \left(7 + \frac{\sin(\pi t)}{\pi}\right) dt \] Calculating the integral gives us: \[ s(t) = 7t - \frac{\cos(\pi t)}{\pi^2} + C \] Now, we need to determine the constant \( C \) using the initial position condition \( s(0) = 5 \): \[ s(0) = 7(0) - \frac{\cos(0)}{\pi^2} + C = 5 \] \[ C - \frac{1}{\pi^2} = 5 \] \[ C = 5 + \frac{1}{\pi^2} \] Substituting back into the position equation, we find: \[ s(t) = 7t - \frac{\cos(\pi t)}{\pi^2} + 5 + \frac{1}{\pi^2} \] \[ s(t) = 7t + 5 + \frac{1 - \cos(\pi t)}{\pi^2} \] Thus, the exact position function is: \[ s(t) = 7t + 5 + \frac{1 - \cos(\pi t)}{\pi^2} \]