What is the average speed of an object that is still at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = \frac{t}{4} + 2$ $a(t) = t/4+2$ from $t \in [0, 6]$ $t in [0, 6]$ ?

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Answer 1 · 2016-03-18T19:49:40

$v_{a} = 7, 5 \frac{m}{s}$ $v_a=7,5" " m/s$

$1- Find displacement at interval (0,6)$ $"1- Find displacement at interval (0,6)"$
$"2-use the formula :"v_a=(Delta x)/(Delta t)$

$v(t)=int a(t) d t" ; "x=int_a^b v(t)d t$

$v(t)=int(t/4+2)d t=1/4*1/2 t^2+2t+C$
$v(t)=1/8 t^2+2t+C" for t=0 ; v=0 ; C=0"$
$v(t)=1/8t^2+2t$

$Delta x=int_0^6(1/8t^2+2t)d t$

$Delta x=|1/8*1/3*t^3+2*1/2*t^2|_0^6$
$Delta x=(1/24*6^3+6^2)-(0+0)$

$Delta x=9+36$
$Delta x=45$

$v_a=45/(6-0)$
$v_a=45/6$
$v_a=7,5" " m/s$

What is the average speed of an object that is still at t=0t=0t=0 and accelerates at a rate of a(t) = t/4+2a(t)=t4+2a(t) = t/4+2 from t in [0, 6]t∈[0,6]t in [0, 6]?