What is the average speed of an object that is still at t=0 and accelerates at a rate of a(t) =t/6+5 from t in [0, 2]?

Apr 22, 2016

Answer:

${v}_{a} = 6 , 5 \text{ unit/s}$

Explanation:

${v}_{a} = \frac{1}{2 - 0} {\int}_{0}^{2} \left(\frac{t}{6} + 5\right) d t$

${v}_{a} = \frac{1}{2} \left[| \frac{1}{6} \cdot {t}^{2} / 2 + 5 t {|}_{0}^{2}\right]$

${v}_{a} = \frac{1}{2} \left[\left(\frac{1}{12} \cdot {2}^{2} + 5 \cdot 2\right) - \left(0\right)\right]$

${v}_{a} = \frac{1}{2} \left[3 + 10\right]$

${v}_{a} = \frac{1}{2} \cdot 13$

${v}_{a} = 6 , 5 \text{ unit/s}$