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

Sep 29, 2016

I found: $v = 3 \frac{m}{s}$

#### Explanation:

I would try integrating your acceleration to obtain the speed as:

$v \left(t\right) = {\int}_{0}^{2} \left(\frac{t}{2} + 1\right) \mathrm{dt} =$

$= \frac{1}{2} {t}^{2} / 2 + t = {t}^{2} / 4 + t$

evaluated between the two extremes:

${v}_{0 \to 2} = \left(\frac{4}{4} + 2\right) - 0 = 1 + 2 = 3 \frac{m}{s}$