Find the position and velocity of an object moving along a sfraight line with the given accesteration, initial velocity, and initial position. \[ a(t)=\cos \pi t, v(0)=7, s(0)=5 \] The velocity is \( v(t)=\square \) (Type an exact answer.)

To find the velocity, we need to integrate the acceleration function \( a(t) = \cos(\pi t) \). Integrating \( a(t) \): \[ v(t) = \int a(t) \, dt = \int \cos(\pi t) \, dt = \frac{1}{\pi} \sin(\pi t) + C \] Using the initial condition \( v(0) = 7 \): \[ v(0) = \frac{1}{\pi} \sin(0) + C = 7 \implies C = 7 \] Thus, the velocity function is: \[ v(t) = \frac{1}{\pi} \sin(\pi t) + 7 \]