What is the average speed of an object that is still at $t=0$ and accelerates at a rate of $a(t) =2t^2-t-4$ from $t in [2, 3]$ ?

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Answer 1 · 2017-03-24T07:44:27

The average speed is $=6.17ms^-1$

$a(t)=2t^2-t-4$

Velocity is

$v(t)=int(2t^2-t-4)dt$

$=2/3t^3-1/2t^2-4t+C$

Initial conditions, $v(0)=0$

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

So,

$C=0$

Average speed is

$barv*(3-2)=int_2^3(2t^2-t-4)dt$

$=[2/3t^3-1/2t^2-4t]_2^3$

$=(18-9/2-12)-(16/3-2-8)$

$=6-9/2-16/3+10$

$=16-59/6$

$=37/6$

The average speed is $=6.17ms^-1$

What is the average speed of an object that is still at t=0t=0 and accelerates at a rate of a(t) =2t^2-t-4a(t) =2t^2-t-4 from t in [2, 3]t in [2, 3]?