What is the average speed of an object that is still at $t=0$ and accelerates at a rate of $a(t) = t$ from $t in [0,3]$ ?

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Answer 1 · 2017-12-31T13:05:18

The average speed is $=1.5ms^-1$

The speed is the integral of the acceleration

$a(t)=t$

Therefore,

$v(t)=inta(t)dt=inttdt=t^2/2+C$

Plugging in the initial conditions

$v(0)=0$

$v(0)=0+C$ , $=>$ , $C=0$

Therefore,

$v(t)=t^2/2$

The average speed in the interval $t in [0, 3]$ is

$3 barv=int_0^3t^2/2dt=[t^3/6]_0^3=(27/6)-(0)$

$barv=9/6=3/2=1.5ms^-1$

What is the average speed of an object that is still at t=0t=0 and accelerates at a rate of a(t) = ta(t) = t from t in [0,3]t in [0,3]?