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

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Answer 1 · 2016-05-11T19:50:04

$v_a=17/6" " m/s$

$(d v)/(d t)=a(t)$

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

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

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

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

$v=t^2/2-4t+5$

$(d x)/(d t)=v(t)$

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

$int d x=int _4^5 v(t)*d t$

$x=int_4^5 (t^2/2-4t+5)d t$

$x=|1/2*t^3/3-4*t^2/2+5*t|_4^5$

$x=(1/2*5^3/3-2*5^2+5*5)-(1/2*4^3/3-2*4^2+5*4)$

$x=125/6-50+25)-(64/6-32+20)$

$x=125/6-25-64/6+12=61/6-13$

$x=(61-78)/6$

$x=|-17/6|$

$x=17/6 meters$

$v_a=x/t$

$v_a=(17/6)/(5-4)$

$v_a=17/6" " m/s$

What is the average speed of an object that is moving at 5 m/s5 m/s at t=0t=0 and accelerates at a rate of a(t) =t-4a(t) =t-4 on t in [4,5]t in [4,5]?