Velocity over time with constant power

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SUMMARY

The discussion centers on the relationship between velocity and time for a car operating under constant power conditions. The derived equation for velocity as a function of time is confirmed as v = √(2Pt/m), where P represents power, t is time, and m is mass. The participants agree that this results in a root graph, illustrating the direct correlation between power and velocity over time. The derivation also emphasizes the connection between power, force, and acceleration in the context of classical mechanics.

PREREQUISITES
  • Understanding of basic physics concepts, particularly kinetic energy and power.
  • Familiarity with calculus, specifically derivatives and integrals.
  • Knowledge of classical mechanics, including force, mass, and acceleration.
  • Ability to interpret mathematical equations and graphs.
NEXT STEPS
  • Study the principles of kinetic energy and its relationship to power in physics.
  • Explore the derivation of equations of motion under constant acceleration.
  • Learn about graphing functions, particularly root graphs, in mathematical analysis.
  • Investigate the implications of constant power on real-world vehicle dynamics.
USEFUL FOR

Physics students, automotive engineers, and anyone interested in the dynamics of motion under constant power conditions.

watarok
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For a car with constant power, how will its velocity change over time?

Since power (P) is the derivative of the kinetic energy (Ek), I've found that the equation for the velocity as a function of time is √(2*P*t/m). Is this correct? Would the graph then be a root graph?
 
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so P = F*v, which means v = P/F. and F = mdv/dt... therefore vdv=Pdt/m which leads to v=\sqrt{(2Pt/m)}, so yeah I think you've got it right.
 

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