Question

A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time is proportional to:
(i) t¹/²
(ii) t
(iii) t³/²
(iv) t².

Answer 1

Answer:

Option 3 is correct.

Explanation:  

Since it is given that a body is moving unidirectionally under the influence of a source of constant power and we know that power is defined as rate of doing work.so,

$P=\frac{W}{T}$..........................................(1)

Where W=work done, T=Time taken

$W=F\times d$............................................(2)

d=displacement, F=Applied force

$F=m\times a$..............................................(3)

m=mass of body, a=acceleration

$a=\frac{V}{t}$..................................................(4)

V=velocity of body, t=time taken

$V=\frac{d}{t}$...................................................(5)

d=displacement of body

put equation 2,3,4 and 5 IN 1,we get

$P=\frac{md^{2} }{t^3}$

since power is constant and mass is also a constant we get,

$d=\sqrt{\frac{P}{m} } \times t^\frac{3}{2}$

So option 3 is correct