1. Where the two particles involved start at the same point and the same time.

Use  to write down expressions for S_A and S_B, the distances travelled by A and B in time t respectively.
 

The condition for overtaking is:   SA = SB

2. Where the two particles start at the same time but one starts behind the other. i.e. there is a distance lag.

Use  to write down expressions for S_A and S_B, the distances travelled by A and B in time t respectively.
 

The condition for overtaking is:       SB = SA + d

3. Where the particles start at the same point but at different times. i.e. there is a time lag.
The condition for overtaking is the same as in 1 above i.e. S_A = S_B
The difference is that the times are not the same. Let’s say B starts t seconds after A ,then: