Understanding the Concepts

* Newton's Second Law: This law states that the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a): F = ma

* Equal Acceleration: Both cars have the same acceleration, meaning they are speeding up at the same rate.

Solving the Problem

1. Let's assign variables:

* Let the mass of the smaller car be 'm'

* The mass of the larger car is '2m' (twice the smaller car's mass)

* Let the force applied to the smaller car be 'F1'

* Let the force applied to the larger car be 'F2'

2. Apply Newton's Second Law:

* For the smaller car: F1 = m * a

* For the larger car: F2 = 2m * a

3. Compare the forces:

* Notice that the acceleration 'a' is the same for both cars.

* Since the larger car has twice the mass, the force applied to it (F2) must be twice as large as the force applied to the smaller car (F1).

Conclusion:

To make the two cars accelerate equally, you need to apply twice the force to the larger car compared to the smaller car.