What is the average speed of an object that is still at $t=0$ and accelerates at a rate of $a(t) =3t-4$ from $t in [2, 3]$ ?

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Answer 1 · 2017-07-16T15:13:19

The average speed is $=-0.5ms^-1$

The speed is the integral of the acceleration

$a(t)=3t-4$

$v(t)=int(3t-4)dt=3/2t^2-4t+C$

Plugging in the initial conditions at $t=0$

$v(0)=0-0+C=0$ , $=>$ , $C=0$

The average velocity is

$(3-2)barv=int_2^3(3/2t^2-4t)dt$

$=[1/2t^3-2t^2]_2^3$

$=(27/2-18)-(4-8)$

$barv=-0.5$

What is the average speed of an object that is still at t=0t=0 and accelerates at a rate of a(t) =3t-4a(t) =3t-4 from t in [2, 3]t in [2, 3]?