Need help with question on Equations of Motion

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Please help me with this question:

A cyclist is travelling at a constant speed of 12m/s when she passes a stationary bus. The bus starts moving just as the cyclist passes, and  it accelerates uniformly at 1.5m/s.
a) How long does the bus take to catch up with the cyclist?
b) What distance has the cyclist travelled before the bus catches up?

Thanks in advance 

[Lasercookie]

The best way to approach motion questions when you're stuck is to write out everything you know - including formulae.

So:

A cyclist is travelling at a constant speed of 12m/s when she passes a stationary bus. The bus starts moving just as the cyclist passes, and  it accelerates uniformly at 1.5m/s.

Cyclist:

Bus:

You know that when they catch up, they will be at the same point distance wise.
So:












So using null factor law, t=0 and t=16. We can reject t=0 in this case, since we know that was when they started.
So the answer is t=16 seconds.

For part b, you can just sub 16 into our original equations:
Cyclist:

Bus:

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thanks mate