**One-dimensional Collision**

When the children play marbles, then if one marble collides with another marble and after the collision if the marbles move in a straight line, then that collision is called one-dimensional collision. That means, if the relative motion of the two colliding bode is along the same straight line below and after the collision, then that collision is called one dimensional collision.

Suppose two particles of masses m_{1} and m_{2} are moving in a straight line along x-axis with velocities v_{01} and v_{02} respectively (Figure]. Here v_{01} > v_{02}. At one time the first body hits the second body from behind and afterwards the two particles move along the same straight line with velocities v_{1} and v_{2} respectively.

Here action force applied on the body of mass m_{2} is F_{1} and the mass m_{2} also creates reaction force F_{2} on m_{1}.

Again, suppose if the duration of the action and reaction is t,

then sum of initial momentum of the two particles = m_{1}v_{01} + m_{2}v_{02} … … … (1)

and the sum of the final momentum of the two particles = m_{1}v_{1} + m_{2}v_{2}

According to Newton’s third law of motion,

action = reaction

F_{2} = – F_{1}

During collision the action and reaction forces act for the same duration.

Suppose, the two bodies move along the same straight line, before and after the collision, with velocities v_{01} and v_{02} respectively. Due to action and reaction, accelerations of the two bodies become a_{1} and a_{2}.

then, F_{1} = – F_{2}

or, m_{1}a_{1} = – m_{2}a_{2}

or, m_{1} [(v_{1} – v_{01}) / t] = – m_{2} [(v_{2} – v_{02}) / t]

or, **m _{1}v_{1} – m_{1}v_{01} = – m_{2}v_{2} + m_{2}v_{02}**

According to the principle of conservation of momentum,

Momentum before collision = Momentum after collision.

This is the equation of one-dimensional collision.