What is the average speed of an object that is moving at $9 m/s$ at $t=0$ and accelerates at a rate of $a(t) =2t+1$ on $t in [1,2]$ ?

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Answer 1 · 2018-03-02T09:26:12

The average speed is $=12.83ms^-1$

The speed is the integral of the acceleration

$a(t)=2t+1$

$v(t)=int(2t+1)dt$

$=t^2+t+C$

Plugging in the initial conditions

$v(0)=9$

$v(0)=0+C=9$

$=>$ , $C=9$

Therefore,

$v(t)=t^2+t+9$

The average speed is

$(2-)barv=int_1^2(t^2+t+9)dt$

$barv=[t^3/3+t^2/2+9t]_1^2$

$=(8/3+2+18)-(1/3+1/2+9)$

$=7/3+11-1/2$

$=12.83ms^-1$

What is the average speed of an object that is moving at 9 m/s9 m/s at t=0t=0 and accelerates at a rate of a(t) =2t+1a(t) =2t+1 on t in [1,2]t in [1,2]?