A small car can produce a force of 20,000 N. If the mass of the car is increased because more people get in, what should happen to the possible acceleration of the car?

A. Increase
B. Decrease
C. Stay the same
D. None of these



Answer :

To determine how the acceleration of the car changes when its mass increases, we can use Newton's second law of motion, which states:

[tex]\[ F = m \times a \][/tex]

where:
- [tex]\( F \)[/tex] is the force applied (in Newtons, N)
- [tex]\( m \)[/tex] is the mass of the object (in kilograms, kg)
- [tex]\( a \)[/tex] is the acceleration of the object (in meters per second squared, m/s²)

We know the force ([tex]\( F \)[/tex]) remains constant at 20,000 N. Let's consider two scenarios: the initial mass of the car and the increased mass due to more passengers.

1. Initial Conditions:
- Initial mass ([tex]\( m_1 \)[/tex]): 1000 kg

Using the formula, we calculate the initial acceleration ([tex]\( a_1 \)[/tex]):

[tex]\[ a_1 = \frac{F}{m_1} \][/tex]

Substituting the values:

[tex]\[ a_1 = \frac{20000}{1000} = 20 \, \text{m/s}^2 \][/tex]

2. Increased Mass:
- Increased mass ([tex]\( m_2 \)[/tex]): 1200 kg

Again, using the formula, we calculate the new acceleration ([tex]\( a_2 \)[/tex]) after increasing the mass:

[tex]\[ a_2 = \frac{F}{m_2} \][/tex]

Substituting the values:

[tex]\[ a_2 = \frac{20000}{1200} \approx 16.67 \, \text{m/s}^2 \][/tex]

From these calculations, we observe that the initial acceleration was 20 m/s² and the new acceleration decreased to approximately 16.67 m/s² after increasing the mass.

Therefore, when the mass of the car increases, the possible acceleration of the car decreases.

Hence, the correct answer is:
- Decrease