Question

The power supplied by a force acting on a particle moving in a straight line is constant. The velocity of the particle varies with the displacement x as

Answer 1

Answer:

the best Answer is : x=1/3

Answer 2

velocity of the particle varies with the displacement x as v ∝ x⅓.

it is given that, power supplied by a force acting on a particle moving in a straight line is constant

so, P = F.v = constant

⇒ma × v = P

we know, a = d²x/dt² and v = dx/dt

so, m × d²x/dt² × dx/dt = P

⇒m × d(dx/dt)/dt × dx/dt = P

we know, dm²/dt = 2m dm/dt

so, d(dx/dt)²/dt = 2 × dx/dt × d(dx/dt)/dt

then, m × 1/2 × d(dx/dt)²/dt = P

⇒∫d(dx/dt)² = 2P/m ∫ dt

⇒(dx/dt)² = (2P/m) t

putting, v = dx/dt

so, v = dx/dt = √(2P/m)t½ .......(1)

⇒∫dx = √(2P/m) t½ ∫dt

⇒x = √(2P/m) t^(3/2) .........(2)

from equations (1) and (2) we get,

x ∝ v³

⇒v ∝ x⅓

hence, velocity of the particle varies with the displacement x as v ∝ x⅓