Question

A constant power P is applied to particle of mass m. The distance travelled 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

P = Fv or P = mav or p = m $\left( \frac{vdv}{dx} \right)$v

or P = mv² $\frac{dv}{dx}$ or dx = $\frac{m}{P}$v² dv

or $\int_{0}^{x}{dx = \frac{m}{p}\int_{v_{1}}^{v_{2}}{v^{2}dv}}$

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

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