A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time t is proportional to (i) t⅟² (ii) t (iii) t³/² (iv) t²

The power of the body can be calculated as,

P=[ F ][ v ]

By substituting the dimensional valuesof F and vin the above equation, we get

P=[ MLT -2 ][ LT -1 ] =[ ML 2 T -3 ]

Since the body is moving under the influence of a source of constant power so the values of power and mass will beconstant.

Therefore, the above equation can bewrittenas,

L 2 T -3 =const. L 2 ∝ T 3 L∝ T 3/2

Thus, l∝ t 3/2 and option (iii) is correct.