# What is the average speed of an object that is moving at 2 m/s at t=0 and accelerates at a rate of a(t) =t-1 on t in [1,2]?

Feb 13, 2016

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

#### Explanation:

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