Certainly! To determine the car's new momentum when its velocity doubles, let's follow the step-by-step process:
1. Understanding Momentum: Momentum ([tex]\( p \)[/tex]) is given by the product of an object's mass ([tex]\( m \)[/tex]) and its velocity ([tex]\( v \)[/tex]). Mathematically, this relationship is expressed as:
[tex]\[
p = m \cdot v
\][/tex]
2. Initial Momentum: We are told that the initial momentum of the car is [tex]\( 20,000 \, \text{kg} \cdot \text{m/s} \)[/tex].
3. Doubling the Velocity: If the car’s velocity doubles, we need to determine how the momentum changes. Assume the initial velocity is [tex]\( v \)[/tex]. When the velocity doubles, it becomes [tex]\( 2v \)[/tex].
4. New Momentum Calculation: The new momentum will be the mass of the car times the new velocity. Since the new velocity is [tex]\( 2v \)[/tex], the new momentum ([tex]\( p_{\text{new}} \)[/tex]) will be:
[tex]\[
p_{\text{new}} = m \cdot (2v)
\][/tex]
5. Relating New Momentum to Initial Momentum: Notice that since we had the initial momentum [tex]\( p = m \cdot v = 20,000 \, \text{kg} \cdot \text{m/s} \)[/tex], when the velocity doubles, the new momentum will be:
[tex]\[
p_{\text{new}} = 2 \cdot (m \cdot v) = 2 \cdot 20,000 \, \text{kg} \cdot \text{m/s} = 40,000 \, \text{kg} \cdot \text{m/s}
\][/tex]
6. Conclusion: The car's momentum would be [tex]\( 40,000 \, \text{kg} \cdot \text{m/s} \)[/tex] if its velocity doubles.
Therefore, the correct answer is:
[tex]\[
\boxed{40,000 \, \text{kg} \cdot \text{m/s}}
\][/tex]
