Momentum/velocity physics question

Question

Two toy cars are tied together with with elastic and have a compressed spring between them. When the elastic is cut the cars move apart. If one cart has a mass of 2.3kg and moves with a speed of 80cm/s, find the speed of the other cart if its mass is 3.6kg.

I calculated the answer to be 51cm/s. Correct?

Answer 1

Conservation of momentum:

M(Vt) = m,v, + m,,v,,

The velocity of the center of mass of a system which has no external forces acting on it (the two cars and the spring) does not change. So the sum of the movement of the two cars should equal to the sum of their masses times their total velocity (which starts at zero and will stay there until some external force acts).

(m, + m,,)(0) = ( 2.3 kg )( 80 cm/s ) + ( 3.6 kg )·v,,

0 = ( 2.3 kg )( 80 cm/s ) + ( 3.6 kg )·v,,

-( 2.3 kg )( 80 cm/s ) = ( 3.6 kg )·v,,

-( 2.3 kg )( 80 cm/s )/( 3.6 kg ) = v,,

v,, ≈ -51 cm/s

The speed wouldn't have the sign (while velocity would), so yes, you would be correct.