Hello !

I'm not in MAT270, nor do I know what this stands for... but it doesn't matter

But this is something commonly used in physics.

If f(t) is the position function, then the speed function is . And the velocity (which means speed at an instant) at time t=a is

You can view it this way :

- speed is a ratio distance/time

- the derivative is a ratio "function displacement"/"units"

A formal way to view the velocity is to see that velocity at a time t=a is the difference of distance that occurred instantaneously. More basically, it is the difference of distance that occurred within a very very very little interval of time.

Let be this interval of time.

denotes the difference of distance within this very little time (around t=a). Dividing by will make the speed.

Because we want this interval to be very small, like null, we'll make

So finally, we're looking for , by definition.

Is it clear ?

NB : the acceleration function is