2026 IGCSE Additional Mathematics May/June 0606/23 Q5

In this question time \(t\) is in seconds and lengths are in metres.

A particle moves in a straight line.

When \(t=0\) the particle starts from rest.

The particle moves with constant acceleration until, at \(t=T\), it reaches a velocity of \(V\).

From \(t=T\) until \(t=3T\) the particle moves with constant velocity \(V\).

Then the particle decelerates uniformly and comes to rest at \(t=60\).

1. Sketch the velocity-time graph for the motion, showing all the information given above.[2]
2. It is given that the acceleration during the first part of the journey is 1.5, and the total distance travelled is 1104.
   Find the values of \(T\) and \(V\).[6]