Answer
After picking up the clay, the car slows down by $0.15~m/s$
Work Step by Step
By conservation of momentum, the final momentum of the car and clay is equal to the initial momentum of the car. We can find the final speed of the car and clay:
$m_2~v_2 = m_1~v_1$
$v_2 = \frac{m_1~v_1}{m_2}$
$v_2 = \frac{(120~g)(0.75~m/s)}{120~g+30.0~g}$
$v_2 = 0.60~m/s$
After picking up the clay, the car slows down by $0.15~m/s$.
