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 $\frac{m}{s^{2}}$. a model of the experiment is shown below. 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 ($\frac{m}{s^{2}}$) 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?

Explanation:

Step1: Recall Newton's second - law formula

Newton's second law is $F = ma$, where $F$ is net force, $m$ is mass and $a$ is acceleration. We can solve this formula for $a$ to get $a=\frac{F}{m}$.

Step2: Test the formula with the data

For trial 1: $F = 1.0\ N$, $m = 1.0\ kg$, and $a=\frac{F}{m}=\frac{1.0\ N}{1.0\ kg}=1.0\ \frac{m}{s^{2}}$.
For trial 2: $F = 1.0\ N$, $m = 2.0\ kg$, and $a=\frac{F}{m}=\frac{1.0\ N}{2.0\ kg}=0.5\ \frac{m}{s^{2}}$.
For trial 3: $F = 2.0\ N$, $m = 1.0\ kg$, and $a=\frac{F}{m}=\frac{2.0\ N}{1.0\ kg}=2.0\ \frac{m}{s^{2}}$.
For trial 4: $F = 2.0\ N$, $m = 2.0\ kg$, and $a=\frac{F}{m}=\frac{2.0\ N}{2.0\ kg}=1.0\ \frac{m}{s^{2}}$.

Answer:

$a=\frac{F}{m}$