Perhaps because when we walk we use a little force in pushing us forward. When we walk briskly, we exert more force on ground and ground exerts the same force on us.
Work done = force * distance
So more work done when we exert more force , as the distance is same.
KE = p₁²/2m₁ = p₂² / 2 m₂
p₁²/p₂² = m₁/m₂
p₁/p₂ = √m₁/√m₂
2 m₁ * KE = p₁²
2 m₂ * KE = p₂²
hence, If m₁ > m₂, then p₁ > p₂