Force required to push the car with constant speed:
To push the car on a level road with a constant speed of 10 meters per second, a force of 50 Newton is required. This force is necessary to overcome the frictional forces acting on the car, such as rolling resistance and air resistance.

Force required to make the car accelerate:
To calculate the force required to make the car accelerate at 2 meters per second, we need to use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).

Formula:
F = m * a

Given information:
Mass of the car (m) = 500 kg
Acceleration (a) = 2 m/s^2

Substitute the values into the formula:
F = 500 kg * 2 m/s^2
F = 1000 N

Therefore, a force of 1000 Newton should be applied to make the car accelerate at 2 meters per second.

Explanation:
When the car is moving at a constant speed, the force required to overcome the frictional forces acting on it is equal to the force of friction. In this case, a force of 50 Newton is needed to maintain the constant speed of 10 meters per second.

However, when the car needs to accelerate, an additional force is required. This force is necessary to overcome the inertia of the car and increase its velocity. According to Newton's second law of motion, the force required to accelerate an object is directly proportional to its mass and the desired acceleration.

In this scenario, the mass of the car is given as 500 kg, and the desired acceleration is 2 meters per second. By substituting these values into the formula F = m * a, we find that a force of 1000 Newton is required to make the car accelerate at the given rate.

It is important to note that this force is in addition to the force required to overcome frictional forces. Therefore, the total force required to push the car with an acceleration of 2 meters per second would be the sum of the force required to overcome friction (50 N) and the force required for acceleration (1000 N), resulting in a total force of 1050 Newton.