A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in 4 s is (1/3)α²√P m. The value of α will b e ______.
Physics · Work , Power and Energy · Power & Its Applications
JEE Mains 30 January 2023 Shift 2 Evening Shift

Question

A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in 4 s is (1/3)α²√P m. The value of α will b e ______.

Physics · Work , Power and Energy · Power & Its Applications

JEE Mains 30 January 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

Power P = dK/dt gives (1/2)mv² = Pt. With m=2 kg, v=√(Pt). Then dx/dt = √(Pt). Integrating from 0 to 4 s gives x = √P × (2/3) t ( 3 / 2 ) ∣ 0 4 t^(3/2)|₀⁴ t ( 3/2 ) ∣ 0 4 ​ = (16/3)√P. Comparing with (1/3)α²√P gives α²=16, so α=4.