Answer
The velocity of the center of mass is $98.0~m/s$
Work Step by Step
We can find the velocity of each object after $10.0~s$:
$v_f = v_0+at = 0+(9.80~m/s^2)(10.0~s) = 98.0~m/s$
We can find the velocity of the center of mass $v_{com}$:
$v_{com} = \frac{(3.0~kg)(98.0~m/s)+(4.0~kg)(98.0~m/s)}{3.0~kg+4.0~kg} = 98.0~m/s$
The velocity of the center of mass is $98.0~m/s$
