It is possible we are misunderstanding your question. You say that after the collision the heavy cart “got a greater velocity”. Many have answered as if you were surprised that the heavier cart had greater velocity than it started with, i.e. zero. That is to say you were surprised the larger cart had any velocity at all. However, from your follow on posts it sounds like you understand that the heavier cart should wind up with some velocity, but perhaps you are surprised by how much velocity.
When you say “greater velocity” what do you mean? Greater than what? What is it about the final velocity of the large cart that surprises you?
If you are saying that it surprises you that the final speed of the heavy cart is greater than the final speed of the lighter cart, then yes, I can see where your intuition might not have expected that, but it is perfectly understandable in terms of the conservation of momentum. The best example of that is the case where the masses are equal. After the collision the incoming cart has no velocity, and the originally stationary cart has all the velocity.
Perhaps part of the reason you are having trouble understanding this is because you wrote your equation wrong. You wrote:
VitaminK said:
Relevant Equations::
m1×v+m2×v= -(m1×Vo)+m2×Vo
That is incorrect. The idea is that the total momentum of the two carts does not change before and after the collisions. You need to distinguish their individual initial and final velocities:
##m_1 v_{1i }+ m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f}##
The initial velocity of the second cart is zero so this becomes
##m_1 v_{1i } = m_1 v_{1f} + m_2 v_{2f}##
The velocities have direction which will come in here as signs.
To go further you need to say something more about the collision. In physics problems they almost always use one of two easy to calculate extremes: A) perfectly elastic implying that energy is conserved or B) perfectly inelastic, implying that the objects stick together and the final velocities are the same.