# Newton second

The newton second (also newton-second, symbol N s or N·s)[1] is the derived SI unit of impulse. It is dimensionally equivalent to the momentum unit kilogram metre per second (kg·m/s). One newton second corresponds to a one-newton force applied for one second.

${\displaystyle {\vec {F}}\cdot t=\Delta m{\vec {v}}}$
newton second
For two objects moving with the same velocity (v), the object with the greater mass (m) will have the greater momentum (p).
General information
Unit systemSI derived unit
Unit ofImpulse and momentum
SymbolN s
Named afterIsaac Newton
In SI base units:kg m/s

It can be used to identify the resultant velocity of a mass if a force accelerates the mass for a specific time interval.

## Definition

Momentum is given by the formula:

${\displaystyle \mathbf {p} =m\mathbf {v} ,}$
• ${\displaystyle \mathbf {p} }$ is the momentum in newton second (N s) or "kilogram meters per second" (kg·m/s)
• ${\displaystyle m}$ is the mass in kilogram
• ${\displaystyle \mathbf {v} }$ is the velocity in meters per second (m/s)
N s = N${\displaystyle \cdot }$ s= kg ${\displaystyle \cdot }$ m/s

## Examples

This table gives the magnitudes of some momenta for various masses and speeds.

Mass
(kg)
Speed
(m/s)
Momentum
newton seconds
Explanation
0.42 2.4 1 A 420 gram football (FIFA specified weight for outdoor size 5) kicked to a speed of 8.6 km/h.
0.42 38 16 The momentum of the famous football kick of the Brazilian player Roberto Carlos in the match against France in 1997. The football had a speed of 137 km/h, making it one of the hardest kicks measured.
1,300 10 13,000 A four-door car weighing 1,300 kg (2,866 lb) crashing at 36 km/h (22.37 mph).
2,000 10 20,000 A mid-size SUV weighing 2,000 kg (4,409 lb) crashing at 36 km/h (22.37 mph).
6 1 6 The total impulse of a class C model rocket engine, which can be found in amateur fireworks.
10 2 20 The total impulse of a class D model rocket engine, which also can be found in amateur fireworks.
2,030,000 8050 1.63x1010 Space Shuttle launched from earth to orbit
45,702 10834 4.95x108 Apollo 11 launched from earth to orbit
0.0075 350 2.6 A 7.5-gram handgun bullet (e.g. 9mm Parabellum) fired at 350 m/s.
0.004 945 3.8 A 4-gram assault rifle bullet (e.g. 5.56×45mm NATO) fired at 945 m/s.
0.05 860 43 A 50-gram machine gun bullet (e.g. .50 BMG) fired at 860 m/s.