Reflect on how conservation of momentum explains the motion in these cases. How can understanding this concept encourage careful and responsible

• Mass of the first cart: $m_1 = 1 \text{ kg}$
• Initial velocity of the first cart: $u_1 = 6 \text{ m/s}$
• Mass of the second cart: $m_2 = 3 \text{ kg}$
• Initial velocity of the second cart (stationary): $u_2 = 0 \text{ m/s}$

For an elastic collision, the total momentum before the collision equals the total momentum after the collision:

Substitute the known values:

For an elastic collision, the relative speed of approach equals the relative speed of separation:

Substitute the known values:

From equation (**), we can express $v_1$ in terms of $v_2$:

Substitute this expression for $v_1$ into equation (*):

Now, substitute the value of $v_2$ back into the expression for $v_1$:

The velocities of both carts after the collision are:

• Velocity of the first cart: $\boxed{\mathbf{v_1 = -3 \text{ m/s}}}$
• Velocity of the second cart: $\boxed{\mathbf{v_2 = 3 \text{ m/s}}}$