Final answer:
The change in momentum of a 1600 kg car decelerating from 20 m/s to 0 m/s is -32000 kg·m/s. The negative sign indicates a direction opposite to the car's initial motion; however, the magnitude is 32000 kg·m/s.
Step-by-step explanation:
The change in momentum of a car can be calculated by using the formula for linear momentum, which is the product of mass and velocity. The momentum before coming to a stop is the mass of the car times its initial velocity, and the momentum after coming to a stop is zero since the final velocity is zero. Thus, the change in momentum (Δp) is simply the initial momentum. For a 1600 kg car slowing from 20 m/s to 0 m/s, the change in momentum is:
Δp = m(v_f - v_i)
Δp = 1600 kg × (0 m/s - 20 m/s)
Δp = 1600 kg × -20 m/s
Δp = -32000 kg·m/s
The negative sign indicates the direction of the change in momentum is opposite to the car's initial motion. It's important to realize that the magnitude of the change in momentum is 32000 kg·m/s, as the sign is just indicative of the direction.