# Impulse and Impulse Force

According to* Newton's Second Law of Motion* - force can be expressed as

F = dM / dt (1)

where

F = applied force (N, lb_{f})

dM = change of momentum (kg m/s, lb ft/s)

dt = time taken (s)

Eq. *(1)* can alternatively be expressed as

* dM = F dt (1b)*

Change in momentum is force times acting time.

Forces that act for a very short time are called impulse forces. The product of the impulsive force and the time it acts is called the impulse. The impulse is equal to the change of momentum caused by the impulsive force and can be expressed as

I = Fdt = dM (2)

where

I = impulse (N s)

### Example - resulting Velocity after an Acting Force

A force *1000 N* is acting on a car with mass *1000 kg* in *10 second*.

The impulse - or change in momentum - can be calculated

*I = dM = (1000 N) (10 s)*

* = 10000 (N s, kg m/s)*

Since *momentum* can be expressed as

M = m v (3)

where

M = momentum (kg m/s, lb ft/s)

m = mass (kg, lb)

v = velocity (m/s, ft/s)

then the velocity of the car after *10 s* can be calculated as

*v = (10000 kg m/s) / (1000 kg)*

* = 10 m/s *

* = 36 km/h *

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