Mass = m , momentum is p = m v. In time Δ t, momentum changes by Δ p, the rate of change of momentum is: Δ p Δ t = Δ ( m v ) t = m Δ v Δ t

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Mass = m , momentum is   p  =  m  v. In time   Δ  t, momentum changes by   Δ  p, the rate of change of momentum is:            Δ      p              Δ      t        =            Δ      (      m      v      )        t    =  m            Δ      v              Δ      t

ralharn · Accepted Answer

1) Yes indeed, the absence of a   Δ in the second expression is just a typo.2) The last expression is derived assuming that mass is a constant. If it helps, just set the mass equal to 4, or something. If we want to know how the quantity 4v  changes, we really only need to know how the quantity v changes. Suppose v changes from       v    1   to       v    2  . Then  Δ  v  =      v    2    −      v    1      ,and what will   Δ  (  4  v  ) be? Why it will be  Δ  (  4  v  )  =  4      v    2    −  4      v    1    =  4  (      v    2    −      v    1    )  =  4  Δ  v    .So the constant comes out the front, because it doesn&#039;t change between the start and end points that you&#039;re considering. Hence it can be factored out.3) It&#039;s important that I point out that            Δ      p              Δ      t        =  m            Δ      v              Δ      t      is not Newton&#039;s second law. It&#039;s just a relationship between the rate of change of momentum and acceleration, and can be derived straight from the definitions of these things. Newton&#039;s second law cannot be derived, and is a statement of real physical content --- hence it is called a law. Newton&#039;s law can be written as either  F  =  m            Δ      v              Δ      t          ,or  F  =            Δ      p              Δ      t          ,whichever you prefer. You can show these two are equivalent using the argument in your textbook (although in fact they&#039;re not quite equivalent, as I established above --- the first equation only holds when mass is constant; the second is more general, and more universally true).

Mass = m, momentum is p=mv. In time Δt, momentum changes by Δp, the rate of change of momentum is: Δp/Δt=Δ(mv)/t=mΔv/Δt

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