We know that the power is given by:

P = Fv

= mav = mv\( \dfrac{dv}{dt}\)

= k (constant)

vdv = \( \dfrac{k}{m}\)dt

On integration:

\( \dfrac{v^2}{2} = \dfrac{k}{m}dt\)

\( v = \sqrt{\dfrac{2kt}{m}}\)

To get the displacement:

v =\( \dfrac{dx}{dt}= \sqrt{\dfrac{2k}{m}} t^{\dfrac{1}{2}}\)

dx = \(k′ t^{\dfrac{1}{2}} dt\)

where \(k′ = \sqrt{\dfrac{2k}{3}}\)

x = \( \dfrac{2}{3}k′ t^{\dfrac{2}{3}}\)

Hence, from the above equation it is shown that \( x ∝ t^{\dfrac{3}{2}}\)

Answered by Pragya Singh | 1 year agoA person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated.

**(a)** How much work does she do against the gravitational force?

**(b)** Fat supplies 3.8 × 10^{7}J of energy per kilogram which is converted to mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?

The windmill sweeps a circle of area A with their blades. If the velocity of the wind is perpendicular to the circle, find the air passing through it in time t and also the kinetic energy of the air. 25 % of the wind energy is converted into electrical energy and v = 36 km/h, A = 30 m^{2} and the density of the air is 1.2 kg m^{-3}. What is the electrical power produced?

A body of mass 0.5 kg travels in a straight line with velocity \( v =ax^\dfrac{3}{2} \) where\( a = 5 m^\dfrac{-1}{2}s^{–1}\) What is the work done by the net force during its displacement from x = 0 to x = 2 m?

A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, the sand starts leaking out of a hole on the floor of the trolley at the rate of0.05 kg s^{–1}. What is the speed of the trolley after the entire sandbag is empty?

The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?