# Convert Acceleration Units

- 1

Current unit

## Acceleration Dimensional Analysis

Acceleration represents the speed rate of change. In other words, the acceleration tells us how much the speed changes over time.

The dimensional analysis stems from the interrelation of two other quantities: speed and time.

```
Acceleration = speed / time
= L¹ / T¹ / T¹
= L¹ T⁻²
```

where `L`

and `T`

represent the fundamental base units of length and time, respectively.

## Commonly Used Acceleration Units

In the International System of Units (SI), the fundamental unit of acceleration is meters per second squared (m/s²). This unit represents the change in an object's velocity in meters per second for every second it accelerates.

In the US and other countries using the imperial system, the prevailing unit is feet per second squared (ft/s²).

Scientists and engineers commonly rely on those two units to communicate acceleration.

## How Acceleration is Measured in Seconds?

Beyond the technical and scientific realms, m/s² and ft/s² seldom find use everyday conversation. In fact, you likely won't overhear discussions about acceleration in terms of distance per time squared while strolling through the mall.

Instead, a more relatable way of communicating acceleration, like when we brag about our brand new car, would be something like this:

My Tesla accelerates from 0 to 60 miles per hour (mph) in just 3 seconds.

That's in fact an acceleration. The speed changes from 0 mph to 60 mph in 3 seconds, which is equivalent to saying:

My Tesla accelerates 20 miles per hour per second (mph/s).

In the regions using metric units, the conversations are similar:

My Tesla accelerates from 0 to 100 kilometers per hour (km/h) in just 3 seconds.

Which is equivalent to:

My Tesla accelerates 33 kilometers per hour per seconds (km/h/s).

## How to Convert Acceleration from Metric to US Units: m/s² to ft/s²

When we dive into converting acceleration units, we find that acceleration relies on two essential aspects: length and time. Time is universally measured in seconds, but different systems use varying units for length.

To understand how this conversion works, we need to go back to historical agreements that set up conversion factors for fundamental units. One significant agreement is the International Yard and Pound Agreement of 1959. This pact standardized how the foot (ft) relates to the metric system. According to this agreement:

```
ft = 0.3048 m
```

Using this known conversion, we can work out a new factor for converting m/s² into ft/s²:

```
ft/s² = 0.3048 m/s²
```

Now, let's make things even clearer. We can divide both sides of the equation by `0.3048 m/s²`

:

```
ft/s² / (0.3048 m/s²) = 1
```

This simple trick allows us to take the left side of the equation as a conversion factor. Applying this conversion factor to an acceleration in m/s², the metric units cancel out, and we're left with the US unit we're aiming for.

Here's an example of how to convert an acceleration of 20 m/s² into ft/s² (US units):

```
20 m/s² · conversion_factor
= 20 m/s² · ft/s² / (0.3048 m/s²)
= 20 / 0.3048 ft/s²
= 65.6167979002624672 ft/s²
```

You probably don't need a precision of 18 digits. Rounding it to six decimals seems enough for most cases:

```
20 m/s² = 65.616798 ft/s²
```

## How to Convert Acceleration from US Units to Metric: ft/s² to m/s²

Using the same procedure, we can convert ft/s² to m/s². We just have to invert the fraction to have in the denominator the units we need to cancel out:

```
0.3048 m/s² / (ft/s²) = 1
```

Here's how to convert an acceleration of 20 ft/s² into metric units:

```
20 ft/s² · conversion_factor
= 20 ft/s² · 0.3048 m/s² / (ft/s²)
= 20 · 0.3048 m/s²
= 6.096 m/s²
```

## Common Acceleration Values

Here you'll find a list of acceleration references to effectively compare orders of magnitude.

Reference | m/s² | ft/s² | From 0 to 60 mph |
---|---|---|---|

Car - Tesla Model S Plaid | 30.3 | 44.4 | 1.98 s |

Car - Ferari SF90 Stradale | 30.0 | 44.0 | 2.0 s |

Car - Porsche 918 Spyder | 28.6 | 41.9 | 2.1 s |

Animal - Cheetah | 8.9 | 29.3 | 3 s |

Human - Usain Bolt | 9.5 | 31.2 | - |

Gravity on Earth | 9.8 | 32.2 | - |