# What is the average speed of an object that is not moving at t=0 and accelerates at a rate of a(t) =t+2 from t in [0, 1]?

Feb 13, 2016

${v}_{a} = 2 , 5 \frac{m}{s}$

#### Explanation:

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