What is the average speed of an object that is moving at $9 m/s$ at $t=0$ and accelerates at a rate of $a(t) =3-t$ on $t in [0,5]$ ?

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Answer 1 · 2018-05-07T14:35:01

The average speed is $=12.33ms^-1$

$a(t)=3-t$

The velocity is the integral of the acceleration

$v(t)=inta(t)dt=int(3-t)dt=3t-1/2t^2+C$

Plugging in the initial conditions

$v(0)=9$

Therefore,

$v(0)=0-0+C=9$

$C=9$

$v(t)=3t-1/2t^2+9$

The average speed on $t in [0,5]$ is

$(5-0)barv=int_0^5(3t-1/2t^2+9)dt$

$(5)barv=[3/2t^2-1/6t^3+9t]_0^5$

$=(75/2-125/6+45)-(0)$

$=185/3$

$barv=185/15=12.33ms^-1$

What is the average speed of an object that is moving at 9 m/s9 m/s at t=0t=0 and accelerates at a rate of a(t) =3-ta(t) =3-t on t in [0,5]t in [0,5]?