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

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

 

[nlightner]

, this is a great question! The reason why the acceleration in Newton's second law is represented as a=(d^2x)/(dt)^2 is because it is the second derivative of position with respect to time. This means that it takes into account the change in velocity over time, which is crucial in understanding the relationship between force, mass, and acceleration. On the other hand, (dx)^2/(dt)^2 only represents the change in position over time, and does not take into consideration the change in velocity. Therefore, it is not a suitable representation for acceleration in Newton's second law. I hope this clarifies your doubt!