Question

a student applies a 1.0 n net force to a 1.0 kg cart. another student measures its acceleration with a motion sensor. the cart’s acceleration is 1.0 \\(\frac{\text{m}}{\text{s}^2}\\). a model of the experiment is shown below.
image of experiment setup with motion sensor, cart, and force sensor
the students repeat their experiment for a total of four trials, using different combinations of mass and net force. their data table is below.

trial number

net force (n)

mass (kg)

acceleration \\(\left(\frac{\text{m}}{\text{s}^2}\

ight)\\) |

1	1.0	1.0	1.0
2	1.0	2.0	0.5
3	2.0	1.0	2.0
4	2.0	2.0	1.0

based on the data, which equation could be a model for how acceleration is related to net force and mass?
choose 1 answer:
a \\(\text{acceleration} = \frac{\text{net force}}{\text{mass}}\\)
b \\(\text{acceleration} = \text{net force} + \text{mass}\\)
c \\(\text{acceleration} = \frac{\text{mass}}{\text{net force}}\\)
d \\(\text{acceleration} = \text{net force} \times \text{mass}\\)

Explanation:

Step1: Test Option A with Trial 1

Using \( \text{acceleration} = \frac{\text{net force}}{\text{mass}} \), substitute \( \text{net force} = 1.0 \, \text{N} \), \( \text{mass} = 1.0 \, \text{kg} \):
\( \text{acceleration} = \frac{1.0}{1.0} = 1.0 \, \frac{\text{m}}{\text{s}^2} \), which matches Trial 1.

Step2: Test Option A with Trial 2

Substitute \( \text{net force} = 1.0 \, \text{N} \), \( \text{mass} = 2.0 \, \text{kg} \):
\( \text{acceleration} = \frac{1.0}{2.0} = 0.5 \, \frac{\text{m}}{\text{s}^2} \), which matches Trial 2.

Step3: Test Option A with Trial 3

Substitute \( \text{net force} = 2.0 \, \text{N} \), \( \text{mass} = 1.0 \, \text{kg} \):
\( \text{acceleration} = \frac{2.0}{1.0} = 2.0 \, \frac{\text{m}}{\text{s}^2} \), which matches Trial 3.

Step4: Test Option A with Trial 4

Substitute \( \text{net force} = 2.0 \, \text{N} \), \( \text{mass} = 2.0 \, \text{kg} \):
\( \text{acceleration} = \frac{2.0}{2.0} = 1.0 \, \frac{\text{m}}{\text{s}^2} \), which matches Trial 4.

Step5: Eliminate Other Options

• Option B: \( \text{acceleration} = \text{net force} + \text{mass} \). For Trial 1: \( 1.0 + 1.0 = 2.0

eq 1.0 \), so invalid.

• Option C: \( \text{acceleration} = \frac{\text{mass}}{\text{net force}} \). For Trial 1: \( \frac{1.0}{1.0} = 1.0 \) (matches), but Trial 2: \( \frac{2.0}{1.0} = 2.0

eq 0.5 \), invalid.

• Option D: \( \text{acceleration} = \text{net force} \times \text{mass} \). For Trial 1: \( 1.0 \times 1.0 = 1.0 \) (matches), but Trial 2: \( 1.0 \times 2.0 = 2.0

eq 0.5 \), invalid.

Answer:

A. \( \text{acceleration} = \frac{\text{net force}}{\text{mass}} \)