Time independent acceleration equation?

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SUMMARY

The discussion centers on the validity of a differential equation related to time-independent acceleration. The equation presented, a = dV/dt = dV/(V dx), is deemed invalid due to unit inconsistencies. The correct formulation is identified as dV/dx = (1/V)dV/dt, leading to the conclusion that acceleration can be expressed as a = V dV/dx. This clarification is crucial for understanding the relationship between velocity and acceleration in physics.

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  • Understanding of differential equations
  • Familiarity with the concepts of acceleration and velocity
  • Knowledge of unit analysis in physics
  • Basic calculus skills
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  • Study the derivation of acceleration equations in classical mechanics
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  • Explore the implications of time-independent acceleration in real-world scenarios
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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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