Practicing Success
The speed v reached by a car of mass m in travelling a distance x, driven with constant power P, is given by : |
\(v = \frac{3xP}{m}\) \(v = (\frac{3xP}{m})^{1/2}\) \(v = (\frac{3xP}{m})^{1/3}\) \(v = (\frac{3xP}{m})^2\) |
\(v = (\frac{3xP}{m})^{1/3}\) |
\(P = Fv = m\frac{dv}{dt} v\) \(\Rightarrow v\frac{dv}{dt} = \frac{P}{m}\) \(\Rightarrow v\frac{dv}{dx}{dx}{dt} = \frac{P}{m}\) \(\Rightarrow v^2 \frac{dv}{dx} = \frac{P}{m}\) \(\Rightarrow v^2 dv = \frac{P}{m} dx\) \(\Rightarrow \int_0^v v^2 dv = \frac{P}{m} \int_0^x dx\) \(\Rightarrow \frac{v^3}{3} = \frac{Px}{m}\) \(\Rightarrow v = (\frac{3xP}{m})^{1/3}\) |