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Newton’s Second Law of Motion

Aug 29, 2022

Key Concepts:

  • Newton’s second law of motion
  • Relate force, mass and acceleration


In this session we are going to learn about second law of motion of Newton. 


Newton’s second law of motion 

Newton’s second law of motion states that the rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which force acts. Force is equal to the product of mass and acceleration. 

F = ma 

Few of the applications are: 

  • A fielder pulls his hand backward while catching a cricket ball coming with a great speed, to reduce the momentum of the ball with a little delay. This reduces the effect of the force exerted by the ball on his hands. 
  • Seat belts prevent injuries when brakes are applied in a fast-moving car. A car has a large momentum due to its large velocity, which is reduced to zero in a very short time, hence provided with seat belts.  
Use of Seat Belt
  • For athletes, during long and high jump, sand bed or cushioned bed is provided to allow a delayed change of momentum to zero to prevent the athletes from being injured due to rapid change in momentum to zero. 
  • A karate player breaks slab of bricks in a single blow as when hands move they carry velocity and when they touch slab the velocity is reduced to 0 in a very short time. Hence, the force exerted is very high and the slab breaks in a single blow. 
Karate Player


One Newton: 

One Newton is defined as that force necessary to provide a mass of one kilogram with an acceleration of one meter per second per second squared. 


1 Newton (N) = 1kg × 1m/s2 

1N = kg m/s2 

Derivation of Second Law of Motion 

Let the mass of a moving object be m and F be the force acting on it. 

Let the velocity of the object change from u to v in the interval of time t. 

Moving Object

Momentum = p = Mass × velocity  


Initial momentum = mu 

Final momentum = mv 

Change in momentum = mv – mu = m(v–u) 

Rate of change of momentum = m(v–u)/t  

Force ∝ Rate of change of momentum 

F ∝ m(v–u)/t 

F ∝ ma (because a = (v–u)/t) 

F = kma,  

where k is the constant of proportionality 

F = ma 

(k = 1, m = 1kg, a = 1m/s2) 

Questions and Answers 

Question 1: How much force is  needed to produce an acceleration of 20 m/s² in a body of mass  500 g? 

Question 1 Figure


m = 500 g = 0.5 kg 

a  = 20 m/s² 

F = ? 

F = m × a  

   = 0.5 – 20  

  = 10 N  

Question 2: A body of mass 5 kg is moving  with a uniform velocity of 10 m/s. It is acted upon by a force of 20 N. What will be its acceleration?  

Question 2 Figure


M = 5 kg 

u = 10 m/s, F = 20 N  

F = ma 

a =  F/m 

    = 20/5 

    = 4 m/s² 

Question 3: A body of mass 2 kg is kept at rest. A constant force of 6 N starts acting on it. what will be its acceleration? 

Question 3 Figure



m = 2 kg 

u = 0 m/s 

F = 6 N 

a = F/m  

   = 6/2 

   = 3 m/s²  


  • Newton’s second law of motion – “The rate of change of momentum of a body is directly
    proportional to the applied force and takes place in the direction in which force acts.”
  • F = ma where F is the force applied, m is the mass of the object and a is the acceleration
    of the object
  • One Newton is defined as that force necessary to provide a mass of one kilogram with an
    acceleration of one meter per second per second.


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