6 A car passes a point A travelling at \(10 \mathrm {~m} \mathrm {~s} { } ^ { 1 }\). Its motion over the next 45 seconds is modelled as follows.
- The car's speed increases uniformly from \(10 \mathrm {~ms} { } ^ { 1 }\) to \(30 \mathrm {~ms} { } ^ { 1 }\) over the first 10 s .
- Its speed then increases uniformly to \(40 \mathrm {~m} \mathrm {~s} { } ^ { 1 }\) over the next 15 s .
- The car then maintains this speed for a further 20 s at which time it reaches the point B .
- Sketch a speed-time graph to represent this motion.
- Calculate the distance from A to B .
- When it reaches the point B , the car is brought uniformly to rest in \(T\) seconds. The total distance from A is now 1700 m . Calculate the value of \(T\).