(a) Suppose that the acceleration function of a particle moving along a coordinate line is $a(t) = t-5$. Find the average acceleration of the particle over the time interval $0 \leq t \leq 6$ by integrating.

$a_{\mathrm{ave}}$ $=$

(b) Suppose that the velocity function of a particle moving along a coordinate line is $v(t) = -5\cos\!\left(t\right)$. Find the average acceleration of the particle over the time interval $0 \leq t \leq \frac{\pi}{4}$ algebraically.

$a_{\mathrm{ave}}$ $=$