1.1. A television camera runs on a straight, horizontal rail that lies parallel to the long side $AB$ of a football pitch, where $AB=100m$.

A fixed origin $O$ is taken at the halfway line, with the positive direction from $O$towards $A$.

The motion of the camera is described below.

• At time $t=0$ the camera is at rest at $O$.

• It then moves with a constant velocity so that, at $t=5s$, its displacement from $O$ is $35m$

• The camera remains at this point for a further $3s$

• It then travels back towards $O$ with a constant speed of $10{ms}^{-1}$ until it reaches $O$

• Immediately after passing through $O$ it continues along the rail with a constant velocity of $-2.5{ms}^{-1}$ for $4s$

Determine the displacement of the camera from $O$ at the end of the motion described above and state the total time taken to reach this position.

1.2. Hence determine the total distance travelled by the camera from $t=0$ until it reaches the final displacement found in part (a).