Why is time repeated twice in the unit of acceleration?

In nature, we see that if something moves, it changes its location. It takes some time to complete that movement. So the change in location over a time is defined as speed (or, its rate of change). If the thing is moving in a particular direction then the speed is defined as velocity.

Mathematically, 
Velocity (v) = $\frac{distance (x)}{time (t)} $ 
Velocity is the rate (or speed) an object is moving from A to B over a measurable time.

It's not possible to maintain a constant speed for a very long time. At some point, the speed will increase (or, decrease) or change the direction of motion. All of these changes take place over a time, which are in the form of acceleration.

Mathematically,  
Acceleration (a) = $\frac{velocity (v)}{time (t)} = \frac{distance (x)}{time (t)\; * \;time (t)}$

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

For example: Firstly, we notice that the object change its original position with the certain motion. In the first second, it moved at a speed of 1 meter per second. But after ten seconds, the object travels 2 meters per second. So in 10 seconds, it's speed has increased by 1 meter per second. This is called acceleration.


Finally, let's try to explain this concept in a scientific point of view:

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, time is repeated twice in the unit of acceleration.

Hence, time appears twice: once to describe the rate at which position is changing (i.e. the speed) and once to describe the rate at which the speed is changing.

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