Question

A group of students completed an experiment to study Newton’s second law of motion, by applying force to a toy car and measuring its acceleration. The table below shows the results: Force (N) Acceleration (m/s²) 2.0 5.0 3.0 7.5 6.0 15.0 If these data points were graphed, which conclusion could the students make? Responses The data points will not fall along a line. This shows that as the force increases, the acceleration decreases. The data points will not fall along a line. This shows that as the force increases, the acceleration decreases. - no response given The data points will not fall along a line. This shows that as the force increases, the acceleration increases. The data points will not fall along a line. This shows that as the force increases, the acceleration increases. - no response given The data points will fall along a line. This shows that as the force increases, the acceleration decreases. The data points will fall along a line. This shows that as the force increases, the acceleration decreases. - no response given The data points will fall along a line. This shows that as the force increases, the acceleration increases. The data points will fall along a line. This shows that as the force increases, the acceleration increases. - no response given Skip to navigation

Answer 1

To analyze the provided data according to Newton's second law of motion, which states that Force (F) equals mass (m) times acceleration (a) (F = ma), we can look at how force and acceleration are related in the experiment.

The data points are:

• For 2.0 N, acceleration = 5.0 m/s²
• For 3.0 N, acceleration = 7.5 m/s²
• For 6.0 N, acceleration = 15.0 m/s²

Calculating the ratios of force to acceleration should help us assess the relationship.

1. For 2.0 N: \( \frac{2.0, \text{N}}{5.0, \text{m/s}^2} = 0.4, \text{kg} \)

2. For 3.0 N: \( \frac{3.0, \text{N}}{7.5, \text{m/s}^2} = 0.4, \text{kg} \)

3. For 6.0 N: \( \frac{6.0, \text{N}}{15.0, \text{m/s}^2} = 0.4, \text{kg} \)

In all cases, the ratio of force to acceleration is constant (0.4 kg), which indicates that there is a linear relationship between force and acceleration.

Conclusion:

The correct conclusion that the students could draw is:

The data points will fall along a line. This shows that as the force increases, the acceleration increases.

Thus, the appropriate response is: The data points will fall along a line. This shows that as the force increases, the acceleration increases.