Question 1.3: On the London underground, Oxford Circus and Piccadilly Circ...

On the London underground, Oxford Circus and Piccadilly Circus are 0.8 km apart. A train accelerates uniformly to a maximum speed when leaving Oxford Circus and maintains this speed for 90 s before decelerating uniformly to stop at Piccadilly Circus.
The whole journey takes 2 minutes. Find the maximum speed.

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The sketch of the speed–time graph of the journey shows the given information, with suitable units.

The maximum speed is v ms^{-1}.

The area is \frac{1}{2} (120  +  90) × v = 800

v = \frac{800}{105}

= 7.619

The maximum speed of the train is 7.6  ms^{-1}.

fig 1.23

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