What is the average speed of an object that is still at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = \frac{t}{6} + 5$ $a(t) =t/6+5$ from $t \in [0, 2]$ $t in [0, 2]$ ?

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Answer 1 · 2016-04-22T12:00:05

$v_{a} = 6, 5 unit/s$ $v_a=6,5" unit/s"$

$v_{a} = \frac{1}{2 - 0} \int_{0}^{2} (\frac{t}{6} + 5) d t$ $v_a=1/(2-0)int_0^2(t/6+5)d t$

$v_{a} = \frac{1}{2} [{∣ ∣ ∣ \frac{1}{6} \cdot \frac{t^{2}}{2} + 5 t ∣ ∣ ∣}_{0}^{2}]$ $v_a=1/2[|1/6*t^2/2+5t|_0^2]$

$v_{a} = \frac{1}{2} [(\frac{1}{12} \cdot 2^{2} + 5 \cdot 2) - (0)]$ $v_a=1/2[(1/12*2^2+5*2)-(0)]$

$v_{a} = \frac{1}{2} [3 + 10]$ $v_a=1/2[3+10]$

$v_{a} = \frac{1}{2} \cdot 13$ $v_a=1/2*13$

$v_{a} = 6, 5 unit/s$ $v_a=6,5" unit/s"$

What is the average speed of an object that is still at t=0t=0 and accelerates at a rate of a(t)=t6+5a(t) =t/6+5 from t∈[0,2]t in [0, 2]?