# What is the average speed of an object that is still at t=0 and accelerates at a rate of a(t) = t^2-t+1 from t in [2, 3]?

Feb 4, 2016

${v}_{a} = 5 - 3 = 2$
$\frac{d \left[a \left(t\right)\right]}{d t} = {v}_{a}$
${v}_{a} = {\int}_{2}^{3} \left({t}^{2} - t + 1\right) \cdot d t$
${v}_{a} = | 2 t - 1 {|}_{2}^{3} + C$
if t=0 ; then C=0
${v}_{a} = \left(2 \cdot 3 - 1\right) - \left(2 \cdot 2 - 1\right)$
${v}_{a} = 5 - 3 = 2$