What is the average speed of an object that is still at $t=0$ and accelerates at a rate of $a(t) = 6-t$ from $t in [0, 2]$ ?

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Answer 1 · 2017-04-06T06:15:01

The average speed is $=5.33ms^-1$

The velocity is the integral of the acceleration

$a(t)=6-t$

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

$=6t-t^2/2+C$

We apply the initial conditions to find $C$

$v(0)=0$

Therefore, $C=0$

So,

$v(t)=6t-t^2/2$

We can calculate the average value of the velocity

$(2-0)barv=int_0^2(6t-t^2/2)dt$

$=[3t^2-t^3/6]_0^2$

$=(12-4/3)-(0)$

$=32/3$

$=10.67$

So,

$barv=10.67/2=5.33ms^-1$

What is the average speed of an object that is still at t=0t=0 and accelerates at a rate of a(t) = 6-ta(t) = 6-t from t in [0, 2]t in [0, 2]?