How to solve SUVAT problem without using relative velocity

[rollcast]

Homework Statement

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 there's another method I should have/could have used to solve it?

Homework Equations

SUVAT equations of motion

The Attempt at a Solution

See attachment.

Thanks
AL

 

[gneill]

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

 

[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?

 

[gneill]

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?

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?

 

[rollcast]

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?

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?

 

[gneill]

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?

It amounts to the same thing.