What is the average speed of an object that is moving at $12 m/s$ at $t=0$ and accelerates at a rate of $a(t) =2-3t^2$ on $t in [0,2]$ ?

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Answer 1 · 2017-07-13T06:05:40

The average speed is $=12ms^-1$

The speed is the integral of the acceleration

$a(t)=2-3t^2$

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

Plugging in the initial conditions at $t=0$

$v(0)=0-0+C=12$ , $=>$ , $C=12$

So,

$v(t)=2t-t^3+12$

The average speed is

$2barv=int_0^2(2t-t^3+12)dt$

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

$=(4-4+24)-(0)$

$barv=24/2=12$

The average speed is $barv=12ms^-1$

What is the average speed of an object that is moving at 12 m/s12 m/s at t=0t=0 and accelerates at a rate of a(t) =2-3t^2a(t) =2-3t^2 on t in [0,2]t in [0,2]?