Question

a group of students conduct an experiment to study newton’s second law of motion. they applied a force to a toy car and measure its acceleration. the table shows the results.

force (n)	acceleration (m/s²)
3.0	7.5
6.0	15.0

if the students graph the data points, which conclusion will they be able to make?
(1 point)

• the data points will not 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.
• the data points will not 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

Explanation:

1. First, analyze the relationship between force and acceleration using the given data. Calculate the ratio of force to acceleration for each data point:

• For the first point: $\frac{Force}{Acceleration}=\frac{2.0\ N}{5.0\ m/s^{2}} = 0.4\ kg$ (mass, since $F = ma\Rightarrow m=\frac{F}{a}$).
• For the second point: $\frac{3.0\ N}{7.5\ m/s^{2}}=0.4\ kg$.
• For the third point: $\frac{6.0\ N}{15.0\ m/s^{2}} = 0.4\ kg$.
• Since the mass (the ratio $\frac{F}{a}$) is constant, the relationship between force ($F$) and acceleration ($a$) is linear (from $F = ma$, when $m$ is constant, $F$ and $a$ are directly proportional, so the graph of $F$ vs $a$ will be a straight line).

1. Now, check the trend: as force increases (from 2.0 N to 3.0 N to 6.0 N), acceleration also increases (from 5.0 $m/s^{2}$ to 7.5 $m/s^{2}$ to 15.0 $m/s^{2}$).
2. Evaluate each option:

• Option 1: Incorrect. The data points will fall along a line (since $F$ and $a$ are directly proportional with constant mass), and acceleration increases with force, not decreases.
• Option 2: Incorrect. The data points will fall along a line, but acceleration increases with force, not decreases.
• Option 3: Incorrect. The data points will fall along a line (because of the constant mass and direct proportionality between $F$ and $a$).
• Option 4: Correct. The data points will fall along a line (due to $F = ma$ with constant $m$) and as force increases, acceleration increases.

Answer:

The data points will fall along a line. This shows that as the force increases, the acceleration increases. (Assuming the last option in the original problem is this correct statement, as the original text for the last option seems to be cut off but based on the analysis, this is the correct conclusion.)