# What is the average speed of an object that is still at t=0 and accelerates at a rate of a(t) = t/4+1 from t in [0, 6]?

Nov 11, 2017

"Average" velocity is just the arithmetic mean of the initial and final velocities.
${v}_{a v g} = 7.5$

#### Explanation:

"Acceleration" = ("Velocity")/("time")

$a \left(t\right) = \frac{t}{4} + 1$ ; $\frac{v}{t} = \frac{t}{4} + 1$

$v = {t}^{2} / 4 + t$

${v}_{0} = 0$; ${v}_{6} = {6}^{2} / 4 + 6 = \frac{36}{4} + 6 = 15$

$\frac{{v}_{6} - {v}_{0}}{2} = 7.5$