Two trams, $$\(\operatorname{tram} A\)$$ and tram $$\(B\)$$, run on parallel straight horizontal tracks. Initially the two trams are at rest in the depot and level with each other. At time $$\(t=0, \operatorname{tram} A\)$$ starts to move. Tram $$\(A\)$$ moves with constant acceleration $$\(2 \mathrm{~m} \mathrm{~s}^{-2}\)$$ for 5 seconds and then continues to move along the track at constant speed. At time $$\(t=20\)$$ seconds, tram $$\(B\)$$ starts from rest and moves in the same direction as $$\(\operatorname{tram} A\)$$. Tram $$\(B\)$$ moves with constant acceleration $$\(3 \mathrm{~m} \mathrm{~s}^{-2}\)$$ for 4 seconds and then continues to move along the track at constant speed. The trams are modelled as particles. (a) Sketch, on the same axes, a speed-time graph for the motion of tram $$\(A\)$$ and a speed-time graph for the motion of $$\(\operatorname{tram} B\)$$, from $$\(t=0\)$$ to the instant when $$\(\operatorname{tram} B\)$$ overtakes tram $$\(A\)$$. (3) At the instant when the two trams are moving with the same speed, tram $$\(A\)$$ is $$\(d\)$$ metres in front of $$\(\operatorname{tram} B\)$$. (b) Find the value of $$\(d\)$$. (5) (c) Find the distance of the trams from the depot at the instant when $$\(\operatorname{tram} B\)$$ overtakes $$\(\operatorname{tram} A\)$$. (5)

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