# The acceleration of a sled is 2"m"//"s"^2. What is the acceleration of the sled if we triple the net force and halve the mass?

Aug 13, 2017

$a = 12 {\text{ m"//"s}}^{2}$

#### Explanation:

By Newton's second law, we can state that the acceleration experienced by an object is proportional to the net force acting on it:

$\textcolor{b l u e}{{\vec{F}}_{\text{net}} = m \vec{a}}$

We are given that $a = 2 {\text{ m"//"s}}^{2}$

$\implies F = \left(2 {\text{ m"//"s}}^{2}\right) \cdot m$

Therefore we can solve for acceleration and write:

$\implies 2 {\text{ m"//"s}}^{2} = \frac{F}{m}$

We want to know what happens to the acceleration of the sled if we triple the net force $F$ and halve the mass $m$. Let's see how this would affect the right side of the equation.

$\frac{F}{m}$

$\implies \frac{3 F}{\frac{1}{2} m}$

$\implies \frac{6 F}{m}$

$\implies 6 \left(\frac{F}{m}\right)$

So we can see that tripling $F$ and halving $m$ will lead to a net force which is six times greater than before. Hence, we have:

$a = 6 \cdot \left(2 {\text{ m"//"s}}^{2}\right)$

$= \textcolor{b l u e}{12 {\text{ m"//"s}}^{2}}$