What is the average speed of an object that is moving at $5 m/s$ at $t=0$ and accelerates at a rate of $a(t) =20-t^2$ on $t in [1,5]$ ?

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Answer 1 · 2017-04-04T10:30:40

The average speed is $=52ms^-1$

The velocity is the integral of the acceleration.

$a(t)=20-t^2$

$v(t)=int(20-t^2)dt$

$=20t-t^3/3+C$

We apply the initial conditions to find $C$

$v(0)=5$

Therefore, $C=5$

So,

$v(t)=20t-t^3/3+5$

We can calculate the average value of the velocity

$(5-1)barv=int_1^5(20t-t^3/3+5)dt$

$=[20/2t^2-t^4/12+5t]_1^5$

$=(250-625/12+25)-(10-1/12+5)$

$=(2675/12)-(179/12)$

$=208$

So,

$barv=208/4=52ms^-1$

What is the average speed of an object that is moving at 5 m/s5 m/s at t=0t=0 and accelerates at a rate of a(t) =20-t^2a(t) =20-t^2 on t in [1,5]t in [1,5]?