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

i t1/2  ii t  iii t3/2  iv t2

 

(iii) t1/2

Power is given by the relation:

P = Fv

= mav = mvdvdt = Constant say, k

 vdv = kmdt

Integrating both sides:

vdv=kmdt
v22 = kmt
v = 2ktm
For displacement x of the body, we have:
v = dxdr = 2kmt1/2
dx = k't1/2dt
Where k' = 2k3 = New constant

On integrating both sides, we get:

dx=k't1/2dt
x = 23k't1/2
 x  t3/2