# A 2.0-kilogram cart that is moving due east at 6.0 meters per second collides with a 4.0-kilogram cart moving due west. The carts stick together and move due west at 1.0 meters per second after the collision. What is the initial speed of the of 4.0-kilogram cart before the collision?

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

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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