Force and Rate of Change of Momentum

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Momentum is defined as mass* velocity: p=mv

If we differentiate this expression for the momentum, assuming the mass is constant then

Newton’s Second Law of Motion states that F=ma, so from this this we conclude

  1. which means that the rate of change of momentum equals Force.
  2. Using F=ma we can integrate with respect to time to get(1)

is defined as the impulse, so in English this means, Impulse = change in momentum

We can simplify things by assuming the force and acceleration are constant. This done we can write (1) as


A force of 10N is applied for 5 seconds to a mass of 20 Kg. If the mass starts from rest find the final velocity.


A force of 40N is applied for 5 seconds resulting in an increase of velocity from 2 to 7 m/s . find the mass.

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