What is the average speed of an object that is moving at $2 \frac{m}{s}$ $2 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = t + 1$ $a(t) =t+1$ on $t \in [1, 2]$ $t in [1,2]$ ?

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What is the average speed of an object that is moving at $2 \frac{m}{s}$ $2 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = t + 1$ $a(t) =t+1$ on $t \in [1, 2]$ $t in [1,2]$ ?

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Answer 1 · 2016-02-18T20:36:07

$v = \frac{5}{2} + 2 = \frac{9}{2} \frac{m}{s}$ $v=5/2+2=9/2 m/s$

Explanation:

$v = \int_{1}^{2} a (t) \cdot d t$ $v=int _1^2 a(t)*d t$
$v = \int_{1}^{2} (t + 1) d t$ $v=int _1^2 (t+1)d t$
$v = {[\frac{1}{2} t^{2} + t]}_{1}^{2} + C$ $v=[1/2 t^2+t]_1^2+C$
$v = [2 + 2] - [\frac{1}{2} + 1] + C$ $v=[2+2]-[1/2+1]+C$
$v = 4 - \frac{3}{2} + C$ $v=4-3/2+C$
$v = \frac{5}{2} + C$ $v=5/2+C$
$if t=0 ; v=2; C=2$ $"if t=0 ; v=2; C=2"$
$v = \frac{5}{2} + 2 = \frac{9}{2} \frac{m}{s}$ $v=5/2+2=9/2 m/s$

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What is the average speed of an object that is moving at $2 \frac{m}{s}$ $2 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = t + 1$ $a(t) =t+1$ on $t \in [1, 2]$ $t in [1,2]$ ?

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What is the average speed of an object that is moving at $2 \frac{m}{s}$ $2 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = t + 1$ $a(t) =t+1$ on $t \in [1, 2]$ $t in [1,2]$ ?