A body of mass m starts from rest with a constantpower. If velocity of

1.	A body of mass m starts from rest with a constantpower. If velocity of the body at displacements s is v, then the correct relation is
Answer» Answer: Given: Mass = m Body starts from rest with a constant power p. VELOCITY at displacement s = v To find: Correct relationship Concept: ACCELERATION can be written as follows : $\boxed{acc. = v \times \dfrac{dv}{dx}}$ CALCULATION: Power = Force × Velocity $= > p = f \times v$ $= > p = (m \times acc.) \times v$ $= > p = (m \times v \times \dfrac{dv}{dx} ) \times v$ $= > p = m {v}^{2} ( \dfrac{dv}{dx})$ $= > dx =( \dfrac{m}{p} ) \times {v}^{2} dv$ INTEGRATION on both sides: $= > \int dx =( \dfrac{m}{p} ) \times \int{v}^{2} dv$ Taking limits on integration : $= > \int_{0}^{s} dx =( \dfrac{m}{p} ) \times \int_{0}^{v}{v}^{2} dv$ $= > s = \dfrac{m}{p} \times \dfrac{ {v}^{3} }{3}$ $= > s = \dfrac{m {v}^{3} }{3p}$ So final answer : $\boxed{\large{ \red{s = \dfrac{m {v}^{3} }{3p}}}}$