Let's solve the problem step-by-step.
First, we need to understand the relationship between momentum and velocity. Momentum ([tex]\( p \)[/tex]) is defined as:
[tex]\[ p = m \cdot v \][/tex]
where [tex]\( m \)[/tex] is the mass of the car and [tex]\( v \)[/tex] is its velocity.
Given that the initial momentum ([tex]\( p_{\text{initial}} \)[/tex]) of the car is [tex]\( 20,000 \, \text{kg} \cdot \text{m} / \text{s} \)[/tex]:
[tex]\[ p_{\text{initial}} = 20,000 \, \text{kg} \cdot \text{m} / \text{s} \][/tex]
If the velocity of the car doubles, we can denote the new velocity as [tex]\( 2v \)[/tex]. Since the mass of the car remains unchanged, we can write the new momentum ([tex]\( p_{\text{final}} \)[/tex]) as:
[tex]\[ p_{\text{final}} = m \cdot (2v) \][/tex]
Notice that doubling the velocity will also double the momentum. Therefore:
[tex]\[ p_{\text{final}} = 2 \cdot (m \cdot v) = 2 \cdot p_{\text{initial}} \][/tex]
Given [tex]\( p_{\text{initial}} = 20,000 \, \text{kg} \cdot \text{m} / \text{s} \)[/tex]:
[tex]\[ p_{\text{final}} = 2 \cdot 20,000 \, \text{kg} \cdot \text{m} / \text{s} \][/tex]
[tex]\[ p_{\text{final}} = 40,000 \, \text{kg} \cdot \text{m} / \text{s} \][/tex]
Therefore, if the car's velocity doubles, its momentum would be:
[tex]\[ 40,000 \, \text{kg} \cdot \text{m} / \text{s} \][/tex]
So, the correct answer is:
[tex]\[ 40,000 \, \text{kg} \cdot \text{m} / \text{s} \][/tex]
