# What is the average speed of an object that is still at t=0 and accelerates at a rate of a(t) = 2t^2-t+4 from t in [0,2]?

Apr 29, 2016

${v}_{a} = 5 , 57$

#### Explanation:

${v}_{a} = \frac{1}{{t}_{2} - {t}_{1}} {\int}_{{t}_{1}}^{{t}_{2}} a \left(t\right) \cdot d t$

${v}_{a} = \frac{1}{2 - 0} {\int}_{0}^{2} \left(2 {t}^{2} - t + 4\right) \cdot d t$

v_a=1/2 [|2*t^³/3-t^2/2+4t|_0^2]

$\text{assume t=0; v=0}$

${v}_{a} = \frac{1}{2} \left[\left(2 \cdot {2}^{3} / 3 - {2}^{2} / 2 + 4 \cdot 2\right) - \left(0\right)\right]$

${v}_{a} = \frac{1}{2} \left[\frac{16}{3} - 2 + 8\right]$

${v}_{a} = \frac{1}{2} \left[\frac{16}{3} + 6\right]$

${v}_{a} = \frac{1}{2} \left[\frac{16 + 18}{3}\right]$

${v}_{a} = \frac{1}{2} \left[\frac{34}{3}\right]$

${v}_{a} = \frac{34}{6}$

${v}_{a} = 5 , 57$