Question

A constant power P is applied to a particle of mass m. The distance traveled by the particle when its velocity increases from v₁ to v₂ is (Neglect friction) :

• A. $\frac{3P}{m}(v_{2}^{2} - v_{1}^{2})$
• B. $\frac{m}{3P}(v_{2} - v_{1})$
• C. $\frac{m}{3P}(v_{2}^{3} - v_{1}^{3})$
• D. $\frac{m}{3P}(v_{2}^{2} - v_{1}^{2})$

Answer 1

Answer: (C)

$\frac{m}{3P}(v_{2}^{3} - v_{1}^{3})$

Answer 2

Q P = Fv = mav = m$\left( v\frac{dv}{ds} \right)$v Ž v²dv = $\frac{p}{m}$ds

Ž$\int_{v_{1}}^{v_{2}}{v^{2}dv} = \frac{p}{m}\int_{o}^{s}{ds}$Ž$\frac{v_{2}^{3} - v_{1}^{3}}{3} = \frac{p}{m}$s Ž s = $\frac{m}{3p}(v_{2}^{3} - v_{1}^{3})$