Question
The mass and acceleration of three motorboats were recorded in a table. All motorboats use the same motor. Which result is likely miscalculated?
Relationship Between Mass and Acceleration
Mass (kg) Acceleration (m/s²)
800 750
1200 500
1400 250
(1 point)
Responses
the acceleration or mass of the first boat
the acceleration or mass of the first boat
no miscalculation
no miscalculation
the acceleration or mass of the second boat
the acceleration or mass of the second boat
the acceleration or mass of the third boat
Relationship Between Mass and Acceleration
Mass (kg) Acceleration (m/s²)
800 750
1200 500
1400 250
(1 point)
Responses
the acceleration or mass of the first boat
the acceleration or mass of the first boat
no miscalculation
no miscalculation
the acceleration or mass of the second boat
the acceleration or mass of the second boat
the acceleration or mass of the third boat
Answers
Answered by
GPT-4o mini
To determine if there is a miscalculation, we can analyze the relationship between mass and acceleration given that they both use the same motor. According to Newton's second law, Force (F) = Mass (m) × Acceleration (a). If all boats are using the same motor, they should provide the same force output.
Let’s calculate the force for each motorboat and see if there's a discrepancy:
1. For the first boat (800 kg, 750 m/s²):
\[ F = m \times a = 800 \, \text{kg} \times 750 \, \text{m/s²} = 600,000 \, \text{N} \]
2. For the second boat (1200 kg, 500 m/s²):
\[ F = 1200 \, \text{kg} \times 500 \, \text{m/s²} = 600,000 \, \text{N} \]
3. For the third boat (1400 kg, 250 m/s²):
\[ F = 1400 \, \text{kg} \times 250 \, \text{m/s²} = 350,000 \, \text{N} \]
From the calculations, we see:
- The first boat and the second boat both yield a force of 600,000 N.
- The third boat yields a significantly lower force of 350,000 N.
Since all motorboats use the same motor, they should ideally produce the same force. Thus, the results for the third boat's acceleration or mass is likely miscalculated because it doesn't align with the expected relationship between mass and acceleration for the same motor.
Therefore, the correct response is:
**the acceleration or mass of the third boat.**
Let’s calculate the force for each motorboat and see if there's a discrepancy:
1. For the first boat (800 kg, 750 m/s²):
\[ F = m \times a = 800 \, \text{kg} \times 750 \, \text{m/s²} = 600,000 \, \text{N} \]
2. For the second boat (1200 kg, 500 m/s²):
\[ F = 1200 \, \text{kg} \times 500 \, \text{m/s²} = 600,000 \, \text{N} \]
3. For the third boat (1400 kg, 250 m/s²):
\[ F = 1400 \, \text{kg} \times 250 \, \text{m/s²} = 350,000 \, \text{N} \]
From the calculations, we see:
- The first boat and the second boat both yield a force of 600,000 N.
- The third boat yields a significantly lower force of 350,000 N.
Since all motorboats use the same motor, they should ideally produce the same force. Thus, the results for the third boat's acceleration or mass is likely miscalculated because it doesn't align with the expected relationship between mass and acceleration for the same motor.
Therefore, the correct response is:
**the acceleration or mass of the third boat.**