Answer:
a) The kinetic energy of the two cars is the same
the moment of car 2 is greater than the moment of car 1
b)  the kinetic energy of car 1 is greater than that of car 2
the moment of the two cars is the same
Explanation:
a) to know the kinetic energy of each car, we must find the speed, use Newton's second law to find the acceleration
 Car 1
      F = m a
     a = F / m
Let's use kinematics to find the velocity after x = 1 m
        v² = v₀² + 2 a x
The initial speed is zero
        v = √ (2 F/m  x)
For the distance of x = 1 m
         v₁ = √ (2 F / m)
Car 2
       F = 2m a
       a = F / 2m
       v² = 2 a x
       v = √ (F/m  x)
  For x = 1 m
        v₂ = √(F / m)
Let's calculate the kinetic energy of each car
Car 1
       K₁ = ½ m v₁²
       K₁ = ½ m 2F / m
       K₁ = F
Car 2
       K₂ = ½ 2m v₂²
       K₂ = ½ 2m F / m
       K₂ = F
The kinetic energy of the two cars is the same
Let's calculate the moment
Car 1
    P₁ = m v₁
    P₁ = m √ (2F / m)
Car 2
     P₂ = 2m v²
     P₂ = 2m √(F / m)
We see that the moment of car 2 is greater than the moment of car 1
b) in this part the force is applied by t = 10 s
 Acceleration is the same, let's find the speed
 Car1
           v = v₀ + a t
           v = F / m t
           v₁ = F / m 10
Car 2
            v₂ = F / 2m 10
            v₂ = F / m 5
Let's calculate the kinetic energy of each car
Car 1
            K₁ = ½ m v₁²
            K₁ = ½ m (F / m 10)²
            K₁ = 50 F² / m
Car2
          K₂ = ½ 2m v₂²
          K₂ = m (F / m 5)²
          K₂ = 25 F² / m
In this case we see that the kinetic energy of car 1 is greater than that of car 2
Let's calculate the moment
 Car 1
          P₁ = m v₁
          P₁ = m F / m 10
          P₁ = 10 F
   
Car 2
         P₂ = 2m v₂
         P₂ = 2m F / m 5
         P₂ = 10 F
In this case the moment of the two cars is the same