What is the average speed of an object that is moving at $8 m/s$ at $t=0$ and accelerates at a rate of $a(t) =5-6t$ on $t in [0,2]$ ?

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Answer 1 · 2017-06-04T07:12:29

The average speed is $=9ms^-1$

The speed is the integral of the acceleration

$a(t)=5-6t$

$v(t)=int(5-6t)dt$

$v(t)=5t-6/2t^2+C$

$v(t)=5t-3t^2+C$

Plugging in the initial conditions

$v(0)=0-0+C=8$

So,

$C=8$

and

$v(t)=5t-3t^2+8$

The average speed is

$2barv=int_0^2(5t-3t^2+8)dt$

$=[5/2t^2-3/3t^3+8t]_0^2$

$=(10-8+16)-(0)$

$=18$

$barv=(18)/2=9ms^-1$

What is the average speed of an object that is moving at 8 m/s8 m/s at t=0t=0 and accelerates at a rate of a(t) =5-6ta(t) =5-6t on t in [0,2]t in [0,2]?