What is the average speed of an object that is not moving at t=0 and accelerates at a rate of a(t) =10-2t on t in [3, 5]?

Feb 16, 2016

${v}_{a} = 4$

Explanation:

${v}_{a} = {\int}_{3}^{5} a \left(t\right) d t$
${v}_{a} = {\int}_{3}^{5} \left(10 - 2 t\right) d t$
${v}_{a} = {\left[10 t - {t}^{2}\right]}_{3}^{5} + C$
$\text{for t=0 ; v=0; then C=0}$
${v}_{a} = \left[10 \cdot 5 - {5}^{2}\right] - \left[10 \cdot 3 - {3}^{2}\right]$
${v}_{a} = \left(50 - 25\right) - \left(30 - 9\right)$
${v}_{a} = 25 - 21$
${v}_{a} = 4$