Question

a 3 kg cart moving at 2 m/s collides with a stationary 2 kg cart. if they stick together after the collision, what will be their final velocity? $m_1v_{i1} + m_2v_{i2} = (m_1 + m_2)v_f$
0.8 m/s
1.2 m/s
3.0 m/s
2.0 m/s

Explanation:

Step1: List given values

$m_1=3\ \text{kg}$, $v_{i1}=2\ \text{m/s}$, $m_2=2\ \text{kg}$, $v_{i2}=0\ \text{m/s}$

Step2: Substitute into momentum formula

$$(3)(2) + (2)(0) = (3+2)v_f$$

Step3: Simplify and solve for $v_f$

$$6 = 5v_f \implies v_f=\frac{6}{5}=1.2\ \text{m/s}$$

Answer:

1.2 m/s