# The net force on an object of 14000"N" causes it to accelerate at a rate of 5"m"//"s"^2. What is the mass of the object?

Sep 12, 2017

$m = 2800 \text{kg}$

#### Explanation:

By Newton's second law, force is given by the product of an object's mass and acceleration as:

${\vec{F}}_{\text{net}} = m \vec{a}$

Which we can solve for mass (taking magnitudes) as:

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

We are given:

• $\mapsto a = 5 {\text{m"//"s}}^{2}$
• $\mapsto F = 14000 \text{ N}$

Therefore, we have:

$m = \left(14000 {\text{N")/(5"m"//"s}}^{2}\right)$

$\implies \textcolor{b l u e}{m = 2800 \text{kg}}$

And we can check that the units work out, as we should get our final mass in kilograms.

$k g = \frac{\frac{k g m}{s} ^ 2}{\frac{m}{s} ^ 2}$

$\implies k g = \frac{k g \cancel{m}}{\cancel{s}} ^ 2 \cdot {\cancel{s}}^{2} / \cancel{m}$

$\implies k g = k g$