section_path: Definition in classical mechanics/Relation to force
section_name: Relation to force
paragraph_text: Relation to force
  
  If the net force F applied to a particle is constant, and is applied for a time interval Δ t, the momentum of the particle changes by an amount Δ p = F Δ t. {\displaystyle \Delta p=F\Delta t\,.}
  
  In differential form, this is Newton's second law; the rate of change of the momentum of a particle is equal to the instantaneous force F acting on it, F = d p d t. {\displaystyle F={\frac {{\text{d}}p}{{\text{d}}t}}.}
  
  If the net force experienced by a particle changes as a function of time, F (t), the change in momentum (or impulse J) between times t and t is Δ p = J = ∫ t 1 t 2 F (t) d t. {\displaystyle \Delta p=J=\int _{t_{1}}^{t_{2}}F(t)\,{\text{d}}t\,.}
  
  Impulse is measured in the derived units of the newton second (1 N⋅s = 1 kg⋅m/s) or dyne second (1 dyne⋅s = 1 g⋅cm/s)
  
  Under the assumption of constant mass m, it is equivalent to write
  
  F = d (m v) d t = m d v d t = m a, {\displaystyle F={\frac {{\text{d}}(mv)}{{\text{d}}t}}=m{\frac {{\text{d}}v}{{\text{d}}t}}=ma,}
  
  hence the net force is equal to the mass of the particle times its acceleration.
  
  Example: A model airplane of mass 1 kg accelerates from rest to a velocity of 6 m/s due north in 2 s. The net force required to produce this acceleration is 3 newtons due north. The change in momentum is 6 kg⋅m/s due north. The rate of change of momentum is 3 (kg⋅m/s)/s due north which is numerically equivalent to 3 newtons.