**Momentum**

The momentum is given by the following equation:

Momentum = mass × velocity

p= mv

Since it depends on the velocity and not the speed, momentum is a vector quantity. Momentum is measured in kilogram per second, kg m/s or kgms^{-1}.

**Conservation of momentum**

In an isolated system i.e. if no external force is acting on it, the linear momentum is conserved.

Total momentum before = total momentum after

In the given situation in the diagram, car 1 and 2 travel to the right with the initial velocities u_{1 }and u_{2} respectively. Car 1 catches up to car 2 and they collide. After the collision the cars continue to move to the right but car 1 now travels at velocity v_{1} and car 2 with v_{2}.

Since momentum is conserved,

Total momentum before= total momentum after

M_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1 }+ m_{2}v_{2 } (this is in perfectly elastic collision)

In perfectly elastic collision kinetic energy is conserved and in inelastic collision the kinetic energy is not conserved.

**Explosions**

It is similar to collision, the total momentum before is equal to the total momentum after. In the explosions the total momentum before is zero.

The momentum is given by;

M_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}

Since the momentum before is zero, equation becomes,

0 = m_{1}v_{1} + m_{2}v_{2}

But since v_{1} is negative due to explosion,

0 = -m_{1}v_{1 }+ m_{2}v_{2}

M_{1}v_{1 }= m_{2}v_{2}