What is the average speed of an object that is moving at $9 m/s$ at $t=0$ and accelerates at a rate of $a(t) =2t-5$ on $t in [1,4]$ ?

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Answer 1 · 2017-04-01T05:40:25

The average speed is $=3.5ms^-2$

$a(t)=2t-5$

The speed is the integral of the acceleration

$v(t)=int(2t-5)dt$

$v(t)=2/2t^2-5t+C$

Initial conditions are,

$v(0)=9$

Therefore,

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

So,

$v(t)=t^2-5t+9$

The average velocity is $barv$

$(4-1)barv=int_1^4(t^2-5t+9)dt$

$3barv=[t^3/3-5/2t^2+9t]_1^4$

$=(64/3-40+36)-(1/3-5/2+9)$

$3barv=52/3-41/6=63/6=21/2$

$barv=7/2ms^-1$

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-5a(t) =2t-5 on t in [1,4]t in [1,4]?