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Question

A metro train runs from station A to B to C. It takes $$4$$ min travelling from station A to station B. The train halts at station B for $$20\,s.$$ Then it starts from station B and reaches station C in next $$3$$ minutes. At the start, the train accelerates for $$10$$ sec to reach the constant speed of $$72\,km/hr.$$ The train moving at the constant speed is brought to rest in $$10$$ sec. at next station. (i) Plot the velocity-time graph for the train travelling from the station A to B to C. (ii) Calculate the distance between the stations A, B and C.


Solution

$$AB = 4.6 \,km$$
$$BC = 3.4\,km$$
$$AC = 8\,km$$
Train takes $$10$$ sec to reach $$72\,km/h$$
$$72\dfrac{km}{h} = 22 \times \dfrac{5}{10} = 20\,m/s$$
time travel with constant speed
$$4 \times 60 - 10 - 10 = 220\,sec$$
$$Q = \dfrac{20}{10} = 2\,m/s^2$$
distance from A to B
$$= \dfrac{20^2}{2 \times 2} + 20 \times 220 + \dfrac{20^2}{2 \times 2}$$
$$= 100 + 4400 + 100$$
$$= 4600\,m = 4.6\,km$$
Distance from B to C
$$\dfrac{20^2}{2 \times 2} + 20 \times 160 + \dfrac{20^2}{2 \times 2}$$
$$= 100 + 320 + 100$$
$$= 3400 \,m = 3.4\,km$$
Distance from A to C
$$A - B = 3.4\,km$$
$$B - C = 4.6\,km$$
$$A - C = 8\,km$$

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