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
[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
