# What is the average speed of an object that is still at t=0 and accelerates at a rate of a(t) = t^3-2t+2 from t in [2, 3]?

Feb 1, 2016

${v}_{a} = 15$

#### Explanation:

${v}_{a} = {\int}_{2}^{3} \left({t}^{3} - 2 \cdot t + 2\right) \mathrm{dt}$
${v}_{a} = | 3 {t}^{2} - 2 {|}_{2}^{3}$
${v}_{a} = \left(3 \cdot {3}^{2} - 2\right) - \left(3 \cdot {2}^{2} - 2\right)$
${v}_{a} = \left(3 \cdot 9 - 2\right) - \left(3 \cdot 4 - 2\right)$
${v}_{a} = \left(27 - 2\right) - \left(12 - 2\right)$
${v}_{a} = 25 - \left(10\right)$
${v}_{a} = 25 - 10$
${v}_{a} = 15$