What is the average speed of an object that is not moving at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 10 - 2 t$ $a(t) =10-2t$ on $t \in [3, 5]$ $t in [3, 5]$ ?

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What is the average speed of an object that is not moving at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 10 - 2 t$ $a(t) =10-2t$ on $t \in [3, 5]$ $t in [3, 5]$ ?

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Answer 1 · 2016-02-16T20:19:54

$v_{a} = 4$ $v_a=4$

Explanation:

$v_{a} = \int_{3}^{5} a (t) d t$ $v_a=int _3^5 a(t)d t$
$v_{a} = \int_{3}^{5} (10 - 2 t) d t$ $v_a=int _3^5 (10-2t)d t$
$v_{a} = {[10 t - t^{2}]}_{3}^{2} + C$ $v_a=[10t-t^2]_3^5+C$
$for t=0 ; v=0; then C=0$ $"for t=0 ; v=0; then C=0"$
$v_{a} = [10 \cdot 5 - 5^{2}] - [10 \cdot 3 - 3^{2}]$ $v_a= [10*5-5^2]-[10*3-3^2]$
$v_{a} = (50 - 25) - (30 - 9)$ $v_a=(50-25)-(30-9)$
$v_{a} = 25 - 21$ $v_a=25-21$
$v_{a} = 4$ $v_a=4$

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What is the average speed of an object that is not moving at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 10 - 2 t$ $a(t) =10-2t$ on $t \in [3, 5]$ $t in [3, 5]$ ?

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What is the average speed of an object that is not moving at t=0t=0t=0 and accelerates at a rate of a(t) =10-2ta(t)=10−2ta(t) =10-2t on t in [3, 5]t∈[3,5]t in [3, 5]?

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What is the average speed of an object that is not moving at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 10 - 2 t$ $a(t) =10-2t$ on $t \in [3, 5]$ $t in [3, 5]$ ?