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

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

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Answer 1 · 2016-03-18T20:35:29

$v_{a} = 8, 5 \frac{m}{s}$ $v_a=8,5 " "m/s$

Explanation:

$1 - find v(t) function$ $1-"find v(t) function"$
$v (t) = \int a (t) d t = \int (6 - t) d t = 6 t - \frac{1}{2} t^{2} + C$ $v(t)=int a(t) d t=int (6-t)d t=6t-1/2t^2+C$
$for t=0 v=0 C=0$ $"for t=0 v=0 C=0"$
$v (t) = 6 t - \frac{1}{2} t^{2} + 0$ $v(t)=6t-1/2t^2+0$
$2 - find displacement between t=0 and t=2$ $2-"find displacement between t=0 and t=2"$
$Delta x=int _0^2 v(t) d t$

$Delta x=int _0^2 (6t-1/2t^2)d t=|6*1/2 t^2-1/2*1/3*t^3|_0^2$

$Delta x=(3*2^2-1/6*2^2)-(0-0)$
$Delta x=12-4/6=(72-4)/6=68/4=17$
$3-"find "v_a=(Delta x)/(Delta t)$

$v_a=17/(2-0)$
$v_a=17/2$

$v_a=8,5 " "m/s$

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

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

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