Show that Newton's Second Law is valid?

[Tonia]

Homework Statement

In a laboratory frame of reference, an observer notes that Newton's 2nd Law is valid.
Show that Newton's 2nd Law is also valid for an observer moving at a constant speed, small compared with the speed of light, relative to the laboratory frame.

Homework Equations

dx'/dt = dx/dt - v

The Attempt at a Solution

d^2 x' / dt^2 = d^2 x/ dt^2 Can someone help me understand this better?

 

[Chestermiller]

Homework Statement

In a laboratory frame of reference, an observer notes that Newton's 2nd Law is valid.
Show that Newton's 2nd Law is also valid for an observer moving at a constant speed, small compared with the speed of light, relative to the laboratory frame.

Homework Equations

dx'/dt = dx/dt - v

The Attempt at a Solution

d^2 x' / dt^2 = d^2 x/ dt^2 Can someone help me understand this better?

Which part don't you understand?

Chet

 

[Tonia]

I don't understand the whole answer. Can you explain what each part means?

 

[Tonia]

I know it means derivative but that's it.

 

[Tonia]

The velocity is subtracted from the derivative because it has to be smaller than the speed of light? Also, why is the d squared on the second part and why is d^2x` divided by dt/2 and why does this equal: d^2 x/ dt^2??

 

[Esteban]

The second derivative of $x$ is the acceleration $a$. Considering that the second Newton's law states that $F=ma$, your acceleration doesn't varies because you have added a constant. So, the second Newton's law is valid in this reference frame.

Also, you are mistaken with the notation. $d^2x/dt^2$ means "second derivative of x respect to time".