Question

Solve the following problem.

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

Answer 1

The metro train travels from station A to station B in 4 minutes = 240 s.
The trains halts at station B for 20 s.
The train travels from station B' to station C in 3 minutes = 180 s.
∴ Total time taken by the metro train in travelling from station A to B to C
= 240 + 20 + 180 = 440 s.
At the start, the train accelerates for 10 seconds to reach a constant speed of 72 km/hr = 20 m/s.

The train moving is brought to rest in 10s at the next station.
The velocity-time graph for the train travelling from station A to B to C is as follows:
Distance travelled by the train from station A to station B

= Area of PQRS

= A(Δ PQQ') + A(`square` Q'QRR') + A(SRR')

`= (1/2 xx 10xx20) + (220 xx 20) + (1/2 xx 10 xx 20)`

= 100 + 4400 + 100

= 4600 m

= 4.6 km

∴ Distance travelled by the train from station B' to station C

= Area of EFGD

= A(ΔEFF') + A(`square` F'FGG') + A(Δ DGG')

`= (1/2 xx 10 xx 20) xx (160 xx 20) + (1/2 xx 10 xx 20)`

= 100 + 3200 + 100

= 3400 m

= 3.4 km