# How to solve SUVAT problem without using relative velocity

1. Feb 15, 2012

### rollcast

1. The problem statement, all variables and given/known data
Calculate the time taken for particle A to catch up with particle B.
See attachment for variables.

I worked out the answer by finding the relative velocity of A wrt B but apparently theres another method I should have/could have used to solve it?

2. Relevant equations

SUVAT equations of motion

3. The attempt at a solution

See attachment.

Thanks
AL

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2. Feb 15, 2012

### Staff: Mentor

You could write separate expressions for the positions of each particle, then equate them to find when the positions are the same.

3. Feb 15, 2012

### rollcast

So call the final displacement when they meet, x, get 2 equations and then solve them as simultaneous equations?

Is there any advantage to that approach compared to just working out the relative velocity?

4. Feb 15, 2012

### Staff: Mentor

Either approach could be transformed into the other via suitable algebraic slight of hand. The separate equation approach has the advantage that it may be more straightforward when the particle motions are more complicated. For example, suppose that both particles also had separate accelerations?

5. Feb 15, 2012

### rollcast

But the relative approach will still work with accelerations?

Do you just work out the acceleration of one relative to the other or do you have to use v=u+at for both and then then subtract the 2?

6. Feb 15, 2012

### Staff: Mentor

It amounts to the same thing.