Answer
At $t = 3.0~s$, the center of mass is a distance of $~~22.0~m~~$ from the traffic light.
Work Step by Step
We can find the distance of the car from the traffic light at $t = 3.0~s$:
$d = \frac{1}{2}at^2$
$d = \frac{1}{2}(4.0~m/s^2)(3.0~s)^2$
$d = 18.0~m$
We can find the distance of the truck from the traffic light at $t = 3.0~s$:
$d = v~t$
$d = (8.0~m/s)(3.0~s)$
$d = 24.0~m$
We can find the distance of the center of mass from the traffic light at $t = 3.0~s$:
$com = \frac{(1000~kg)(18.0~m)+(2000~kg)(24.0~m)}{1000~kg+2000~kg}$
$com = 22.0~m$
At $t = 3.0~s$, the center of mass is a distance of $~~22.0~m~~$ from the traffic light.
