2003

1 (a).  The points p, q and r all lie in a straight line.
A train passes point p with speed u m/s. The train is traveling with uniform retardation f m/s². The train takes 10 seconds to travel from p to q and 15 seconds to travel from q to r, where |pq|=|qr|=125 metres.

               (i). Show that f = 1/3.

             (ii). The train comes to rest s metres after passing r.

Find s, giving your answer correct to the nearest metre.

ANSWER

1 (a) (i)

For the first simultaneous equation, consider the journey |pq|.
For the second, consider the journey |pr|.

The journey |pq|.

  No “v”    i.e.

i.e.            Equation A

The journey |pr|.

  No “v”    i.e.

1(a) (ii)

We need to find the total distance, s, i.e. when v = 0.
To do this we must find u.
The required distance is then s – 250.

    No “t”      i.e.

Thus the distance travelled after point r is given by 302.46-250 = 52.46 m