What is the average speed of an object that is moving at $30 \frac{m}{s}$ $30 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 5 - 2 t^{2}$ $a(t) =5-2t^2$ on $t \in [0, 5]$ $t in [0,5]$ ?

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What is the average speed of an object that is moving at $30 \frac{m}{s}$ $30 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 5 - 2 t^{2}$ $a(t) =5-2t^2$ on $t \in [0, 5]$ $t in [0,5]$ ?

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Answer 1 · 2016-02-10T17:51:47

$V = - 28, 3 \frac{m}{s}$ $V=-28,3 m/s$

Explanation:

$v = \int a \cdot d t$ $v=int a *d t$
$v = \int_{0}^{5} (5 - 2 t^{2}) \cdot d t$ $v= int_0^5 (5-2t^2)*d t$
$v = {[5 \cdot t - \frac{2 \cdot t^{3}}{3}]}_{0}^{5} + C$ $v=[5*t-(2*t^3)/3]_0^5+C$
$v = [5 \cdot 5 - \frac{2 \cdot 5^{3}}{3}] - [0] + C$ $v=[5*5-(2*5^3)/3]-[0]+C$
$t = 0; v = 30; C = 30$ $t=0 ;v=30 ;C=30$
$v = 25 - \frac{250}{3} + 30$ $v=25-250/3+30$
$v = 55 - \frac{250}{3}$ $v=55-250/3$
$v = \frac{165 - 250}{3}$ $v=(165-250)/3$
$V = - 28, 3 \frac{m}{s}$ $V=-28,3 m/s$

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What is the average speed of an object that is moving at $30 \frac{m}{s}$ $30 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 5 - 2 t^{2}$ $a(t) =5-2t^2$ on $t \in [0, 5]$ $t in [0,5]$ ?

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What is the average speed of an object that is moving at 30ms30 m/s at t=0t=0 and accelerates at a rate of a(t)=5−2t2a(t) =5-2t^2 on t∈[0,5]t in [0,5]?

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What is the average speed of an object that is moving at $30 \frac{m}{s}$ $30 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 5 - 2 t^{2}$ $a(t) =5-2t^2$ on $t \in [0, 5]$ $t in [0,5]$ ?