Time independent acceleration equation?

AI Thread Summary
The discussion revolves around the validity of a differential equation for time-independent acceleration. It highlights that the original equation presented is incorrect due to unit inconsistencies, as dV/dt represents acceleration while dV/(V dx) has units of inverse length. A suggested correction is dV/dx = (1/V)dV/dt, which aligns with the proper dimensional analysis. The participant acknowledges their mistake and clarifies the correct relationship as a = dV/dt = V dV/dx. This exchange emphasizes the importance of unit consistency in physics equations.
re444
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Hi,

Is this differential equation valid for time independent acceleration"

a = dV/dt = dV/ (V dx) = ( dV / dx ) * (1/V) ?
 
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re444 said:
d = dV/dt = dV/ (V dx) = ( dV / dx ) * (1/V) ?
It's not quite clear what you're doing here. dV/dt has units of acceleration, while dV/(V dx) has units of 1/length. So your equation isn't valid.

Perhaps you're thinking of dV/dx = (1/V)dV/dt ?
 
Doc Al said:
It's not quite clear what you're doing here. dV/dt has units of acceleration, while dV/(V dx) has units of 1/length. So your equation isn't valid.

Perhaps you're thinking of dV/dx = (1/V)dV/dt ?

Oh ! my obvious fault: a = dV / dt = dV/ (dx / V) = V dV/dx .

thanks
 

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