What is the average speed of an object that is moving at $3 m/s$ at $t=0$ and accelerates at a rate of $a(t) =t^2-1$ on $t in [0,2]$ ?

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Answer 1 · 2017-05-08T12:21:21

The average speed is $=2.67ms^-1$

The speed is the integral of the acceleration

$a(t)=t^2-1$

$v(t)=int(t^2-1)dt$

$v(t)=1/3t^3-t+C$

Plugging in the initial conditions

$v(0)=0-0+C=3$

So,

$C=3$

and

$v(t)=1/3t^3-t+3$

The average speed is

$2barv=int_0^2(1/3t^3-t+3)dt$

$=[1/12t^4-1/2t^2+3t]_0^2$

$=(16/12-4/2+6)-(0)$

$=16/3$

$barv=(16/3)/2=2.67ms^-1$

What is the average speed of an object that is moving at 3 m/s3 m/s at t=0t=0 and accelerates at a rate of a(t) =t^2-1a(t) =t^2-1 on t in [0,2]t in [0,2]?