motion question (1 Viewer)

[JamesGoh]

Currently, Im studying the Cambridge Mathematics 4 unit book, and have come across a peculiar statement in the mechanics section

The statement is the following

x'' = (1/2)(d²v/dx)

where x" = the second derivative of x with respect to time.

My question to you guys is how does the 1/2 come into the equation?

My first thoughts was that the integral of x with respect to x makes x²/2, however this would only work if x was the only unknown value. In this case, V(x) could be anything from x to x²

 

[jyu]

a= dv/dt = dx/dt dv/dx = v dv/dx = 1/2 dv^2/dv dv/dx = 1/2 dv^2/dx

 

[JamesGoh]

just to be clear that dv^2 is dv x dv not the second derivative of velocity?

 

[HeroicPandas]

Here, re-typed