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 $a(t) =t^2-5$ on $t in [0,3]$ ?

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Answer 1 · 2018-04-25T14:53:08

The average speed is $=3.92ms^-1$

The speed is the integral of the acceleration

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

$v(t)=1/3t^3-5t+C$

Plugging in the initial conditions

$v(0)=8ms^-1$

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

Therefore,

$v(t)=1/3t^3-5t+8$

$v(3)=9-15+8=2$

$v(4)=64/3-20+8=28/3$

The average speed is

$(5-0)barv=int_0^3(1/3t^3-5t+8)dt+v(3)+v(4)$

$5barv=[1/12t^4-5/2t^2+8t]_0^3+2+28/3$

$=27/4-45/2+24+34/3$

$=19.58$

$barv=19.58/5=3.92ms^-1$

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) =t^2-5a(t) =t^2-5 on t in [0,3]t in [0,3]?