In writing this, I have actually worked it out but I thought seeing as I'd already typed it, it would be a nice problem to leave up for anyone studying for the M1 exam next month. I had a problem with part i, mainly because it was one of the dreaded 'show that' questions...Sorry if this is too simple for most...

Cars A & B are approaching the end of a race. A is 1.5km from the finish, is travelling at a speed of 30m/s and is accelerating uniformly at 0.7m/s^2. B is 210km behind A, is travelling at a speed of 40m/s and is accelerating at 0.5 m/s^2.

(i) Show that B overtakes A 285m before the finish.

(ii) Calculate the difference in time between the arrivals of the two cars at the finish.