What is the average speed, on $t in [0,5]$ , of an object that is moving at $8 m/s$ at $t=0$ and accelerates at a rate of $a(t) =5t^2-2t$ on $t in [0,3]$ ?

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Answer 1 · 2017-06-11T06:23:58

The average speed is $=$

The speed is the integral of the acceleration

$a(t)=5t^2-2t$

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

$=5/3t^3-t^2+C$

Plugging in the initial conditions

$v(0)=0-0+C=8$

Therefore,

$v(t)=5/3t^3-t^2+8$

When $t=3$ ,

$v(3)=45-9+8=44ms^-2$

When $t in [3,5]$ , the speed is $=44ms^-1$

The average speed is $=barv$

$5barv=int_0^3(5/3t^3-t^2+8)dt+2*44$

$5barv=[5/12t^4-1/3t^3+8t]_0^3+88$

$5barv=135/4-9+24+88=136.75$

$barv=136.75/5=27.35ms^-1$

What is the average speed, on t in [0,5]t in [0,5], of an object that is moving at 8 m/s8 m/s at t=0t=0 and accelerates at a rate of a(t) =5t^2-2ta(t) =5t^2-2t on t in [0,3]t in [0,3]?