To determine the new momentum of the car when its velocity doubles, let's follow a step-by-step approach:
1. Understand the relationship between momentum and velocity:
Momentum ([tex]\(p\)[/tex]) of an object is given by the product of its mass ([tex]\(m\)[/tex]) and its velocity ([tex]\(v\)[/tex]):
[tex]\[
p = m \cdot v
\][/tex]
2. Initial scenario:
We are given that the initial momentum of the car is [tex]\(p\)[/tex] and its initial velocity is [tex]\(v\)[/tex].
3. Change in velocity:
The problem states that the velocity of the car doubles. Thus, the new velocity ([tex]\(v_{\text{new}}\)[/tex]) will be:
[tex]\[
v_{\text{new}} = 2v
\][/tex]
4. Calculate the new momentum:
Since momentum is mass times velocity, the new momentum ([tex]\(p_{\text{new}}\)[/tex]) when the velocity doubles will be:
[tex]\[
p_{\text{new}} = m \cdot v_{\text{new}}
\][/tex]
Substituting the new velocity:
[tex]\[
p_{\text{new}} = m \cdot (2v)
\][/tex]
5. Factor in initial momentum:
Recall that the initial momentum [tex]\(p\)[/tex] is:
[tex]\[
p = m \cdot v
\][/tex]
Therefore, the new momentum can be written as:
[tex]\[
p_{\text{new}} = 2 \cdot (m \cdot v)
\][/tex]
[tex]\[
p_{\text{new}} = 2p
\][/tex]
So, the new momentum of the car when its velocity doubles is:
[tex]\[
\boxed{2p}
\][/tex]
Thus, the correct answer is [tex]\(2p\)[/tex].
