## Displacement Between Particles Starting to Move at Different Times

If a particle A starting from a point at moves with constant velocity the displacement vector of the particle at time is given by If another particle B starts from some other point a short time seconds later, we will not be able to use the same equation to find the position vector of particle B.

IF THE TWO PARTICLES START AT DIFFERENT TIMES WE CANNOT USE THE SAME TIME WITHOUT MODIFICATION!

For particle B we can write  here for particle B is not the same as for particle A because particle B started a time later than particle A. In fact is the time for which particle B has been travelling and since B started seconds later than A, We can write therefore and We can use this in the following example.

A particle A starts at from with velocity and a particle B starts at from with velocity Find the distance between the particles when  then  then The displacement vector from A to B is When the displacement vector is and the distance between A and B when is  