Question 6.10:

A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time t is proportional to

it1/2iitiiit3/2ivt2

 

(iii) t1/2

Power is given by the relation:

P = Fv

= mav = mvdvdt=Constantsay,k

vdv=kmdt

Integrating both sides:

vdv=kmdt
v22=kmt
v=2ktm
Fordisplacementxofthebody,wehave:
v=dxdr=2kmt1/2
dx=k't1/2dt
Wherek'=2k3=Newconstant

On integrating both sides, we get:

dx=k't1/2dt
x=23k't1/2
xt3/2