# What is the average speed of an object that is not moving at t=0 and accelerates at a rate of a(t) =4-t/2 on t in [2,3]?

Feb 8, 2016

${v}_{a} = \frac{11}{4} \frac{m}{s}$

#### Explanation:

${v}_{a} = {\int}_{2}^{3} \left(4 - \frac{t}{2}\right) d t$
${v}_{a} = {\int}_{2}^{3} 4 \cdot d t - {\int}_{2}^{3} \frac{t \cdot d t}{2} + C$
t=0" then " V=0; C=0
${v}_{a} = \left(4 t {|}_{2}^{3}\right) - \frac{1}{2} \cdot \frac{1}{2} \cdot {t}^{2} {|}_{2}^{3}$
${v}_{a} = \left(4 \cdot 3 - 4 \cdot 2\right) - \left(\frac{9}{4} - \frac{4}{4}\right)$
${v}_{a} = 4 - \left(\frac{5}{4}\right)$
${v}_{a} = \frac{11}{4} \frac{m}{s}$