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 $t in [0, 6]$ ?

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Answer 1 · 2017-11-11T01:40:28

"Average" velocity is just the arithmetic mean of the initial and final velocities.
$v_(avg) = 7.5$

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

$a(t) = t/4 + 1$ ; $v/t = t/4 + 1$

$v = t^2/4 + t$

$v_0 = 0$ ; $v_6 = 6^2/4 + 6 = 36/4 + 6 = 15$

$(v_6 - v_0)/2 = 7.5$

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