Question

instructions
this final exam is cumulative and covers material from the entire course.
from the list of choices, select the one best answer.
multiple attempts not allowed. this test can only be taken once.
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question 21 of 62
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question 21
a net force \\( \vec{f} \\) is required to give an object with mass \\( \boldsymbol{m} \\) an acceleration \\( \vec{a} \\). if a net force \\( 6\vec{f} \\) is applied to an object with mass \\( 3m \\), what is the acceleration on this object?
\\( 2\vec{a} \\)
\\( \vec{a} \\)
\\( 6\vec{a} \\)
\\( 3\vec{a} \\)

Explanation:

Step1: Recall Newton's Second Law

Newton's second law states $\vec{F} = m\vec{a}$. For the first case, $\vec{F} = m\vec{a}$.

Step2: Analyze the new force and mass

In the second case, the force is $6\vec{F}$ and the mass is $3m$. Let the new acceleration be $\vec{a}'$. Using Newton's second law: $6\vec{F} = 3m\vec{a}'$.

Step3: Substitute $\vec{F}$ from Step1

From Step1, $\vec{F} = m\vec{a}$, so substitute into the second equation: $6(m\vec{a}) = 3m\vec{a}'$.

Step4: Solve for $\vec{a}'$

Simplify the equation: $6m\vec{a} = 3m\vec{a}'$. Divide both sides by $3m$: $\vec{a}' = 2\vec{a}$.

Answer:

$2\vec{a}$ (corresponding to the option "2$\vec{a}$")