Question

question 9
a net force $vec{f}$ is required to give an object with mass m an acceleration $vec{a}$. if a net force $6vec{f}$ is applied to an object with mass 2m, what is the acceleration on this object?
$6vec{a}$
$2vec{a}$
$3vec{a}$
$vec{a}$
$4vec{a}$

Explanation:

Step1: Recall Newton's second law

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

Step2: Find the new acceleration

Given a new force $6\vec{F}$ and mass $2m$. Let the new - acceleration be $\vec{a}_{new}$. Using $\vec{F} = m\vec{a}$, we have $6\vec{F}=2m\vec{a}_{new}$. Substitute $\vec{F}=m\vec{a}$ into $6\vec{F}=2m\vec{a}_{new}$, we get $6(m\vec{a})=2m\vec{a}_{new}$.

Step3: Solve for $\vec{a}_{new}$

Divide both sides of the equation $6m\vec{a}=2m\vec{a}_{new}$ by $2m$. Canceling out the $m$ terms, we have $\vec{a}_{new}=\frac{6}{2}\vec{a}=3\vec{a}$.

Answer:

C. $3\vec{a}$