# How fast will an object with a mass of 15 kg accelerate if a force of  72 N is constantly applied to it?

Mar 14, 2018

The acceleration is $4.8 \frac{m}{s} ^ 2$.

#### Explanation:

The formula that describes the relationship discussed in Newton's 2nd Law is

$F = m \cdot a$.

To find acceleration when knowing force and mass, we need to do some algebra on the above formula. Divide both sides by m and cancel where possible.

$\frac{F}{m} = \frac{\cancel{m} \cdot a}{\cancel{m}}$
So
$a = \frac{F}{m}$

If we plug your data into that equation and perform the indicated division, we find that

$a = \frac{F}{m} = \frac{72 N}{15 k g} = 4.8 \frac{N}{k g}$

The usual units for acceleration are $\frac{m}{s} ^ 2$.
$\frac{N}{k g}$ does not look so much like acceleration.
But, if we look at $F = m \cdot a$ we will see that 1 Newton, applied to a mass of 1 kg, will cause acceleration of 1 m/s^2. So the Newton is equivalent to $\frac{k g \cdot m}{s} ^ 2$. That combination of units was named the Newton to honor Isaac.

Therefore,

$a = \frac{F}{m} = 72 \frac{N}{15} k g = 4.8 \frac{N}{k} g = 4.8 \frac{m}{s} ^ 2$

I hope this helps,
Steve

Mar 15, 2018

$4.8 \setminus {\text{m/s}}^{2}$

#### Explanation:

We use Newton's second law of motion here, which states that

$F = m a$

where $m$ is the mass of the object in kilograms, $a$ is the acceleration of the object in ${\text{m/s}}^{2}$, and $F$ is the force acting on the object in newtons.

We need to solve for acceleration, so we can rearrange the equation into

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

Now, plugging in the given values, we get

$a = \left(72 \setminus \text{N")/(15 \ "kg}\right)$

$= 4.8 \setminus {\text{m/s}}^{2}$

So, the object's velocity will keep increasing by $4.8 \setminus \text{m/s}$ every second towards the direction of the force applied.