A collision is an event in which two or more objects exert forces on each other for a short duration of time. It can be either inelastic or elastic collision. A completely inelastic collision is a special case where the two objects stick together and move with a common final velocity after the collision. Here, it is given that the carts stick together after the collision. This implies that it is an inelastic collision.

The inelastic collision formula is given by

`m_1v_1+m_2v_2=(m_1+m_2)v_f`

where

`m_1` is the mass of object 1

`m_2` is the mass of object 2

`v_1` is the velocity of object 1

`v_2` is the velocity of object 2

`v_f` is the final velocity of the two objects.

From the question, we have,

`m_1=2\ kg` , `v_1=6 ` m/s moving due east

`m_2 = 4\ kg`

`V=1` m/s

Here, we have to find out the initial velocity `v_2` of the cart having mass 4kg moving due west.

Substituting the known values in the above formula, we get,

`2 \times 6+4\times v_2=(2+4)\times 1 `

i.e. `12+4v_2=6`

`4v_2=-6`

`v_2=\frac{-6}{4} = -1.5` m/s

Therefore, the initial velocity of the 4kg cart before the collision is -1.5 m/s.

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