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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