# kilogram-meter per second

The kilogram-meter per second (kg · m/s or kg · m · s ^{-1} ) is the standard unit of momentum . Reduced to base units in the International System of Units ( SI ), a kilogram-meter per second is the equivalent of a newton-second (N · s), which is the SI unit of impulse . Although the units are the same in base terms, there is a conceptual difference between momentum and impulse.

As an example of momentum, consider a rocket ship coasting through space at a speed *v* of 10,000 (10 ^{4} ) m/s. Suppose the mass of the ship, *m* , is equal to 10,000 (10 ^{4} ) kg. The forward momentum, *p* , is equal to the product of the mass and the forward speed:

*p* = *mv*

= 10 ^{4} kg x 10 ^{4} m/s = 10 ^{8} kg · m/s

A rule of Newtonian physics states that the impulse imparted to an object is equal to the change in momentum for that object, provided no other forces or effects are involved. Consider the problem of calculating how long to fire the above mentioned space ship's retro rockets to bring it to a halt with respect to an observer who sees its initial momentum as 10 ^{8} kg · m/s. This requires an impulse in the reverse direction of 10 ^{8} N · s. Suppose the ship's retro rockets produce 100,000 (10 ^{5} ) N of force. According to the formula for impulse, where *F* is the force in newtons and *t* is the time in seconds for which the force is applied:

*I* = *Ft* and therefore *t* = *I* / *F*

*t* = (10 ^{8} N · s) / (10 ^{5} N)

= 1000 s

This is equal to 16 minutes and 40 seconds.

Also see the Table of Physical Units .

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