A person brings a mass of 1 kg from infinity to a point A. Initially the mass was at rest but it moves at a speed of 2 m/s as it reaches A. The work done by a person on the mass is –3J. The potential at A is:

-5 J/kg

The work done by the person $W_{ext}=\Delta KE+\Delta PE_{gr}$

$\Rightarrow-3 J=(1 / 2) mv^2+\Delta PE_{gr}$

$\Rightarrow-3 J=(1 / 2) \times 1 \times(2)^2+\Delta P E_{gr}$

$\Rightarrow \Delta P E_{gr}$ = -3 - 2 = -5 J

∴ m(ΔV) = -5 J

Putting m = 1 kg, we obtain ΔV = - 5J/kg

As, V_infinity = 0

hence, $v_A$ = -5 J/kg