Question

A constant force acts on the body of mass m at rest. The velocity v acquired in covering specific distance depends on m as-

Options_
1. V∝m
2. V∝1/m
3. V∝root of m
4. V∝1/root of m

Answer 1

_____________________________________________________________

♦ Newtonian Mechanics ♦

→ Force imposed is • Constant •

→ Newton's Second Law : The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
_____________________________________________________________

  ◘ F = ma 
=> F = m ( dv / dt )
=> ( F / m ) = ( dv / dt )
=> v ∝ ( 1 / m )
____________________________________________________________

 ◘ Momentum is the impetus gained by a moving object and is defined as :
     • p = mv 

 ◙ Force is the rate of change of momentum :-
   • F = ( dp / dt ) => F ∝ p
=> F ∝ mv 
=> v ∝ m⁻¹       [ Since 'F' is constant ] 
_____________________________________________________________

 ► Above are two general proofs for the above .

 → A common confusion is : 
   • https://www.physicsforums.com/threads/313861/
_____________________________________________________________

 → Hope that helps