Question

The speed v reached by a car of mass m, driven with constant power P, is given by :

• A. v = $\frac{3xP}{m}$
• B. v = $\left( \frac{3xP}{m} \right)^{1/2}$
• C. v = $\left( \frac{3xP}{m} \right)^{1/3}$
• D. v = $\left( \frac{3xP}{m} \right)^{2}$

Answer 1

Answer: (C)

v = $\left( \frac{3xP}{m} \right)^{1/3}$

Answer 2

\ P = F.v = m$\left( \frac{vdv}{dx} \right)v$

\ v²dv = $\frac{p}{m}$dx

\ $\int_{0}^{v}{v^{2}dv}$ = $\frac { \mathrm { p } } { \mathrm { m } }$ $\int_{0}^{x}{dx}$Ž $\frac{v^{3}}{3}$ = $\frac{p}{m}$x Ž v = $\left( \frac{3px}{m} \right)^{1/3}$