Question Newton's second Law: F= M * A

[Mark1991]

Hi!

Why is a in F=m*a
equal to a =(d^2 x) / (d t )^2 and not to (d x)^2 / (d t )^2

Mark

 

[D H]

Notation.

The second derivative is

$$a = \frac {dv}{dt} = \frac{d}{dt}(v) = \frac d {dt} \left( \frac {dx}{dt} \right) = \frac d {dt} \left( \frac {d}{dt} (x)\right)$$

Note that if we treated this is a fraction (which it isn't), one could write

$$a = \frac {dd}{(dt)(dt)}(x) = \frac {d^2}{(dt)^2}(x)$$