The diagram shows a velocity-time graph which models the motion of a car. The graph consists of six straight line segments. The car accelerates from rest to a speed of $$\(20 \mathrm{~m} \mathrm{~s}^{-1}\)$$ over a period of $$\(5 \mathrm{~s}\)$$, and then travels at this speed for a further $$\(20 \mathrm{~s}\)$$. The car then decelerates to a speed of $$\(6 \mathrm{~m} \mathrm{~s}^{-1}\)$$ over a period of $$\(5 \mathrm{~s}\)$$. This speed is maintained for a further $$\((T-30) \mathrm{s}\)$$. The car then accelerates again to a speed of $$\(20 \mathrm{~m} \mathrm{~s}^{-1}\)$$ over a period of $$\((50-T) \mathrm{s}\)$$, before decelerating to rest over a period of $$\(10 \mathrm{~s}\)$$. Given that during the two stages of the motion when the car is accelerating, the accelerations are equal, find the value of $$\(T\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

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