# Calculating Acceleration and Speed#

We know that $f=ma$, or $force = mass \times acceleration$, from Newton's Second Law. We want to find acceleration, which is the change in an object's speed over time. It's typically measured in meters per second per second, or meters/second$^2$. 1m/s$^2$ means that the object is moving 1m/s faster every second.

To find acceleration, we can flip $f=ma$ around to get $a=\frac{f}{m}$, or $acceleration=\frac{force}{mass}$.

It's important to note the units for this equation.

• $a$ (acceleration) is measured in m/s$^2$.
• $m$ (mass) is measured in kilograms, not grams!
• $f$ (force) is measured in Newtons.

## Finding Net Force#

The force variable in $f=ma$ is more properly called net force. The net force is the total force an object is experiencing. How do we find this? By adding up all the forces acting on the object.

### Example #1#

We have the following forces acting on an object (note that the +/- signs are tied to the direction of the force):

• +100 Newtons "driving force." This is similar to our locomotive's tractive effort.
• -20 Newtons "air resistance." We haven't discussed this yet, but we'll include it just for example's sake.
• -50 Newtons friction, similar to the rolling resistance of the train.

We add all these forces up with their signs like so:

$100 + (-20) + (-50) = 30$

So the net force acting on this object is 30 Newtons.

## Calculating Acceleration#

Once we have the net force, all we need is the mass, and we can calculate acceleration. Let's keep using the example above, and say that the cube's mass is 5kg.

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

$a=\frac{30}{5}$

$a=6m/s^2$

So with a net force of 30 Newtons, our cube will accelerate at 6m/s$^2$. So the cube's actual speed varies with time, shown in the table below (starting from 0m/s):

Time Speed
0 seconds 0 m/s
1 second 6 m/s
2 seconds 12 m/s
3 seconds 18 m/s