Displacement Between Particles Starting to Move at Different Times

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If a particle A starting from a pointatmoves with constant velocitythe displacement vector of the particle at timeis given byIf another particle B starts from some other pointa short timeseconds 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 asfor particle A because particle B started a time later than particle A. In factis the time for which particle B has been travelling and since B startedseconds later than A,

We can write thereforeand

We can use this in the following example.

A particle A starts atfromwith velocityand a particle B starts at fromwith velocityFind the distance between the particles when

then

then

The displacement vector from A to B isWhenthe displacement vector isand the distance between A and B whenis