What is the average speed of an object that is moving at $5 \frac{m}{s}$ $5 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = t - 4$ $a(t) =t-4$ on $t \in [4, 5]$ $t in [4,5]$ ?

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What is the average speed of an object that is moving at $5 \frac{m}{s}$ $5 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = t - 4$ $a(t) =t-4$ on $t \in [4, 5]$ $t in [4,5]$ ?

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Answer 1 · 2016-05-11T19:50:04

$v_{a} = \frac{17}{6} \frac{m}{s}$ $v_a=17/6" " m/s$

Explanation:

$\frac{d v}{d t} = a (t)$ $(d v)/(d t)=a(t)$

$d v = a (t) \cdot d t$ $d v=a(t)*d t$

$\int d v = \int a (t) \cdot d t$ $int d v=int a(t)* d t$

$v = \int (t - 4) \cdot d t$ $v=int (t-4)*d t$

$v = \frac{t^{2}}{2} - 4 t + C t = 0; v = 5 \frac{m}{s}; c = 5 \frac{m}{s}$ $v=t^2/2-4t +C " "t=0 ;v=5 m/s" ; "c=5 m/s$

$v = \frac{t^{2}}{2} - 4 t + 5$ $v=t^2/2-4t+5$

$\frac{d x}{d t} = v (t)$ $(d x)/(d t)=v(t)$

$d x = v (t) \cdot d t$ $d x=v(t)*d t$

$\int d x = \int_{4}^{5} v (t) \cdot d t$ $int d x=int _4^5 v(t)*d t$

$x = \int_{4}^{5} (\frac{t^{2}}{2} - 4 t + 5) d t$ $x=int_4^5 (t^2/2-4t+5)d t$

$x = {∣ ∣ ∣ \frac{1}{2} \cdot \frac{t^{3}}{3} - 4 \cdot \frac{t^{2}}{2} + 5 \cdot t ∣ ∣ ∣}_{4}^{5}$ $x=|1/2*t^3/3-4*t^2/2+5*t|_4^5$

$x = (\frac{1}{2} \cdot \frac{5^{3}}{3} - 2 \cdot 5^{2} + 5 \cdot 5) - (\frac{1}{2} \cdot \frac{4^{3}}{3} - 2 \cdot 4^{2} + 5 \cdot 4)$ $x=(1/2*5^3/3-2*5^2+5*5)-(1/2*4^3/3-2*4^2+5*4)$

$x = \frac{125}{6} - 50 + 25) - (\frac{64}{6} - 32 + 20)$ $x=125/6-50+25)-(64/6-32+20)$

$x = \frac{125}{6} - 25 - \frac{64}{6} + 12 = \frac{61}{6} - 13$ $x=125/6-25-64/6+12=61/6-13$

$x = \frac{61 - 78}{6}$ $x=(61-78)/6$

$x = ∣ ∣ ∣ - \frac{17}{6} ∣ ∣ ∣$ $x=|-17/6|$

$x = \frac{17}{6} m e t e r s$ $x=17/6 meters$

$v_{a} = \frac{x}{t}$ $v_a=x/t$

$v_{a} = \frac{\frac{17}{6}}{5 - 4}$ $v_a=(17/6)/(5-4)$

$v_{a} = \frac{17}{6} \frac{m}{s}$ $v_a=17/6" " m/s$

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What is the average speed of an object that is moving at $5 \frac{m}{s}$ $5 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = t - 4$ $a(t) =t-4$ on $t \in [4, 5]$ $t in [4,5]$ ?

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What is the average speed of an object that is moving at 5 m/s5ms5 m/s at t=0t=0t=0 and accelerates at a rate of a(t) =t-4a(t)=t−4a(t) =t-4 on t in [4,5]t∈[4,5]t in [4,5]?

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What is the average speed of an object that is moving at $5 \frac{m}{s}$ $5 m/s$ at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = t - 4$ $a(t) =t-4$ on $t \in [4, 5]$ $t in [4,5]$ ?