What is the average speed of an object that is not moving at $t=0$ and accelerates at a rate of $a(t) =8-t$ on $t in [2,5]$ ?

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Answer 1 · 2017-11-25T07:12:55

The average speed is $=21.5ms^-1$

The speed is the integral of the acceleration

$a(t)=8-t$

$v(t)=int(8-t)dt=8t-1/2t^2+C$

Plugging in the initial conditions

$v(0)=0$

so,

$v(0)=8*0-1/2*O+C=0$

$C=0$

$v(t)=8t-1/2t^2$

The average speed on the interval $t in [2,5]$ is

$(5-2)barv=int_2^5(8t-1/2t^2)dt$

$3barv=[8/2t^2-1/6t^3]_2^5$

$3barv=(4*25-1/6*125)-(4*4-1/6*8)$

$3barv=84-125/6+4/3=64.5$

$barv=64.5/3=21.5ms^-1$

What is the average speed of an object that is not moving at t=0t=0 and accelerates at a rate of a(t) =8-ta(t) =8-t on t in [2,5]t in [2,5]?