# Why is acceleration measured in meters / seconds squared?

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97
Jan 22, 2018

See below.

#### Explanation:

Acceleration is calculated by dividing the change in velocity by time. Since velocity can be measured in $\text{m/s}$ and time can be measured in $\text{s}$, the unit is $\text{meters/sec/sec}$ or ${\text{m/s}}^{2}$.

Let's say you speed up from $\text{10 m/s}$ to $\text{25 m/s}$ and it takes you $5$ seconds to do that. Acceleration is

$a = \frac{{v}_{f} - {v}_{i}}{\text{time}}$

Here

• ${v}_{f} = \text{25 m/s}$
• ${v}_{i} = \text{10 m/s}$
• $t = \text{5 s}$

So the acceleration is

 a = ("25 m/s" - "10 m/s")/"5 s" = ("15 m/s")/ "5 s" = "3 m/s"^(2)

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32
EET-AP Share
Apr 20, 2017

Acceleration relates the time it takes to change your speed which is already defined as the time it takes to change your location. So acceleration is measured in distance units over time x time.

#### Explanation:

We have already discovered that when something moves, it changes its location. It takes some time to complete that movement, so the change in location over the time is defined as speed, or its rate of change. If the thing is moving in a particular direction, the speed can then be defined as velocity.

Velocity is the rate or speed an object is moving from A to B over a measurable time.

It is unusual to maintain a constant velocity in a given direction for very long; at some point the speed will increase or decrease, or the direction of motion will change. All of these changes are a form of acceleration. And all of these changes take place over time.

Acceleration is the rate or speed at which an object is increasing or decreasing its velocity over a measurable time.

We can think of acceleration as doing two things at once. We are still moving across a distance over a time, but we are also increasing how fast we are doing it. We are multi-tasking to arrive sooner, so we have to multiply the time x time to calculate the correct numerical value for our acceleration.

We can ensure the units check out: $v =$velocity; $d =$distance;

$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} t =$time; $a =$acceleration

We will use $m \mathmr{and} s$ (meters for distance and seconds for time)

$v = \frac{d}{t} = \frac{m}{s}$ (meters per second or meters divided by seconds)

$a = \frac{v}{t} = \frac{\frac{m}{s}}{s} = \frac{\frac{m}{s}}{\frac{s}{1}} = \frac{m}{s} \cdot \frac{1}{s} = \frac{m}{s \cdot s} = \frac{m}{s} ^ 2$

And the result is meters per second squared.

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