### Q.10:- A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time *t *is proportional to

(i) *t*^{1/2} (ii) *t* (iii) *t*^{3/2} (iv) *t*^{2}

**Answer:-**

As power,

*P*= force × velocity*P*= [

*MLT*

^{-2}] [

*LT*

^{-1}] = [

*ML*

^{2}

*T*

^{-3}]

As,

*P*= [*ML*^{2}*T*^{-3}]= constant

∴

*L*^{2}*T*^{-3}= constantor,

*L*^{2}/*T*^{3}= constant∴

*L*^{2}∝*T*^{3}or,

*L*∝*T*^{3/2}Hence, right choice is (iii)* t*^{3/2}