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# Ask a Teacher

## DERIVE THE FORMILA F=MA? |

According to Newton's second law of motion :The rate of change of momentum of a body can be obtained by dividing the 'change in momentum' by Time taken for change .So, Newton's second law of motion can be expressed as :The rate of change of momentum of a body is directly proportional to the applied force , and takes place in the direction in which the force acts. Force Change in momentum / Time taken Consider a body of mass m having an initial velocity u.The initial momentum of this body will be mu.Suppose a force F acts on this body for time t and causes the final velocity to become v.The final momentum of this body will be mv.Now,the change in momentum of this body is mv - mu and the time taken for change is t.So,according to Newton's second law of motion : F mv - mu / tor F m(v - u)/tBut (v - u)/t represents change in velocity with time which is known as acceleration 'a'.So,by writing 'a' in place of v - u / t in the above relation,we get : F m x a Thus,the force acting on a body is directly proportional to the product of 'mass' of the body and 'acceleration' produced in the body by thye action of the force , and it acts in the direction of acceleration .This is another definition of Newton's second law of motion. The relation F m x a can be turned into an equation by putting in a constant k.Thus, F = k x m x a (where k is a constant )The value of constant k in SI units is 1,so the above equation becomes : F = m x a or Force = mass x accelerationThus Newton's second law of motion gives us a relationship between 'force' and 'acceleration'. |