The speed-time graph in Figure 2 illustrates the motion of a car travelling along a straight horizontal road. At time $$\(t=0\)$$, the car starts from rest and accelerates uniformly for $$\(30 \mathrm{~s}\)$$ until it reaches a speed of $$\(V \mathrm{~m} \mathrm{~s}^{-1}\)$$ The car then travels at a constant speed of $$\(V \mathrm{~m} \mathrm{~s}^{-1}\)$$ until time $$\(t=T\)$$ seconds. (a) Show that the distance travelled by the car between $$\(t=0\)$$ and $$\(t=T\)$$ seconds is $$\(V(T-15)\)$$ metres. (2) A motorbike also travels along the same road. - The motorbike starts from rest at time $$\(\boldsymbol{t}=\mathbf{1 0} \mathrm{s}\)$$ and accelerates uniformly for $$\(40 \mathrm{~s}\)$$ - The acceleration of the motorbike is the same as the acceleration of the car - The motorbike then travels at a constant speed for a further $$\(10 \mathrm{~s}\)$$ before decelerating uniformly until it reaches a speed of $$\(V \mathrm{~m} \mathrm{~s}^{-1}\)$$ at time $$\(T\)$$ seconds (b) On Figure 2, sketch a speed-time graph for the motion of the motorbike. [If you need to redraw your sketch, there is a copy of Figure 2 on page 15.] (2) (c) Show that the constant speed of the motorbike is $$\(\frac{4 V}{3} \mathrm{~m} \mathrm{~s}^{-1}\)$$ (2) At time $$\(t=T\)$$ seconds, the distance travelled by each vehicle is the same. (d) Find the value of $$\(T\)$$ (5)

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