Question

The velocity acquired by a mass m in traveling a certain distance d starting from rest under the acting of a constant force is directly proportional to :- 1) √m. 1/√m

Answer 1

We know that,
F=ma
F=m (dv/dt)
F= m (dv/dt) ×dx/dx
F= mv dv/dx
Fdx=mvdv
Integrate both sides
Fdx=m(v^2/2)
On solving we find
v=√2Fx/m
Thus, v is directly proportional to 1/√m.