What is the average speed of an object that is moving at $22 m/s$ at $t=0$ and accelerates at a rate of $a(t) =t-8$ on $t in [0,2]$ ?

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Answer 1 · 2018-03-17T09:35:17

The average speed is $=3.67ms^-1$

$"Average speed " = "total distance travelled" /" time taken to cover that distance"$

$a(t)=t-8$

The velocity is

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

Plugging in the initial conditions

$v(0)=22ms^-1$

$22=0-0+C$

Therefore,

$v(t)=1/2t^2-8t+22$

The average speed is

$barv=1/(2-0)int_0^2(1/2t^2-8t+22)dt$

$=1/2[1/6t^3-4t^2+22t]_0^2$

$=1/2((1/6*8-16+22)-(0))$

$=3.67ms^-1$

What is the average speed of an object that is moving at 22 m/s22 m/s at t=0t=0 and accelerates at a rate of a(t) =t-8a(t) =t-8 on t in [0,2]t in [0,2]?