What is the average speed of an object that is moving at $15 \frac{m}{s}$ $15 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 7 - 2 t^{2}$ $a(t) =7-2t^2$ on $t \in [0, 3]$ $t in [0,3]$ ?

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What is the average speed of an object that is moving at $15 \frac{m}{s}$ $15 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 7 - 2 t^{2}$ $a(t) =7-2t^2$ on $t \in [0, 3]$ $t in [0,3]$ ?

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Answer 1 · 2016-03-06T20:50:43

$v_{a} = \frac{81}{3} = 27 \frac{m}{s}$ $v_a=81/3=27" " m/s$

Explanation:

$v (t) = \int (a (t) d t$ $v(t)=int(a(t)d t$
$v (t) = \int (7 - 2 t^{2}) d t v (t) = 7 x - \frac{2}{3} t^{3} + C$ $v(t)=int (7-2t^2)d t" "v(t)=7x-2/3t^3+C$
$if t=0" "v=15 m/s" "v(t)=7x-2/3t^3+15$
$Delta x=int_0^3 v(t) d t" "Delta x=int_0^3(7x-2/3t^3+15)d t$
$Delta x=|7/2x^2-2/12t^4+15t|_0^3$
$Delta x=7/2*3^2-2/12*3^4+15*3$
$Delta x=63/2-81/6+45" "Delta x=63/2-27/2+45$
$Delta x=36+45" "Delta x=81$
$v_a=81/3=27" " m/s$

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What is the average speed of an object that is moving at $15 \frac{m}{s}$ $15 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 7 - 2 t^{2}$ $a(t) =7-2t^2$ on $t \in [0, 3]$ $t in [0,3]$ ?

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What is the average speed of an object that is moving at 15 m/s15ms15 m/s at t=0t=0t=0 and accelerates at a rate of a(t) =7-2t^2a(t)=7−2t2a(t) =7-2t^2 on t in [0,3]t∈[0,3]t in [0,3]?

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What is the average speed of an object that is moving at $15 \frac{m}{s}$ $15 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = 7 - 2 t^{2}$ $a(t) =7-2t^2$ on $t \in [0, 3]$ $t in [0,3]$ ?