Three cars, car x, car y, and car z, begin accelerating from rest, at the same time. car x is more massive than car y, which is more massive than car z. the net force exerted on each car is identical. after 10 seconds, which car has the most amount of momentum?

Ah hah !  We can do this the easy way, or we can do it the hard way.

Whereas, in honor of, and pursuant to my natural laziness, I'm going to
do it the easy way, and not even talk about the hard way.  Please fasten
your seat belt.  It may be a boompy ride.

There are a few different ways to calculate the CHANGE in
an object's momentum.  For this particular problem, it's
best to use this equation for "Change in momentum":

CHANGE in momentum = IMPULSE delivered to the object.

Do you remember how to calculate impulse ?

Impulse = (force exerted in the object) x (time the force lasts) 

-- In the question, it says that the same force is exerted on each car,
and they all get it for 10 seconds apiece.

-- Since the force is the same on each car, and the force lasts for
the same amount of time on each car, the IMPULSE delivered to
each car is the same !

-- So the CHANGE IN MOMENTUM is the same for each car.

-- They all started out from 'rest', so each one started with zero momentum.

-- The CHANGE IN MOMENTUM is the same for each car.

-- So at the end of 10 seconds, NO CAR has the 'most momentum'.
All three cars have the SAME momentum.

Do you see why I said that this is the 'easy way' to solve it ?