What is the average speed, on $t in [0,5]$ , of an object that is moving at $10 m/s$ at $t=0$ and accelerates at a rate of $a(t) =2t^2-10$ on $t in [0,3]$ ?

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Answer 1 · 2017-08-06T06:46:00

The average speed is $=1.6ms^-1$

The speed is the integral of the acceleration

$a(t)=2t^2-10$

$v(t)=2/3t^3-10t+C$

Plugging in the initial conditions

$v(0)=0-0+C=10$

Therefore,

$v(t)=2/3t^3-10t+10$ on the interval $I=[0,3]$

The total distance travelled in $5s$ is

$d=int_0^3(2/3t^3-10t+10)dt+v(3)*2$

$=[1/3t^4-5t^2+10t]_0^3+(18-30+10)*2$

$=(27-45+30)+(-4)$

$=8$

The average speed is

$barv=8/5=1.6ms^1$

What is the average speed, on t in [0,5]t in [0,5], of an object that is moving at 10 m/s10 m/s at t=0t=0 and accelerates at a rate of a(t) =2t^2-10a(t) =2t^2-10 on t in [0,3]t in [0,3]?