Question

A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time t is proportional toa. t⁽¹÷²⁾b. tc. t⁽³÷²⁾d. t²

Answer 1

we know, power is the dot product of force and velocity.
e.g., Power = force × velocity

dimension of force = $[MLT^{-2}]$
dimension of velocity = $[LT^{-1}]$

so, P = $[MLT^{-2}][LT^{-1}]$

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

P is constant and m is mass so, it also remains constant for specific body.

so, $L^2T^{-3}$ = constant

or, L²/T³ = constant

or, L² = constant × T³

or, $L\propto T^{3/2}$

hence, displacement is directly proportional to t^3/2 .

hence, option c is correct.

Answer 2

$\mathfrak{\huge{\red{\underline{\underline{Answer :}}}}}$

${\mathrm{time \: t \: is \: proportional \: to \: t^\frac{3}{2}}}$

Hope it Helps !!