. A train leaves city P at 7.00 a.m. and reaches city Q (a distance of 192 km) at 10.00 a.m. On its way, the train passes (without stopping) two stations A and B, 70 km and 150 km from Pat 8.00 a.m. and 9.00 a.m. respectively. Choose the origin of position axis (x = 0) to be at Q, the origin of time axis (t = 0) to be the time it passes station B, the positive direction of x-axis to be from Q to P, the unit of length to be 10 km, and the unit of time to be 1 h; and give (a) the position-time coordinates of the train when it passes A and B; (b) the position-time co- ordinates of the train when it leaves P, and when it reaches Q; (c) the displacement AB; (d) the velocity of the train between A and B (assumed uniform); (e) the distance AB and the speed of the train between A and B; the ratio of P-Q distance to the distance AB.
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Let’s first calculate where train A is at 8 AM. It started at 7AM, at a speed of 20 km/hr. So at 8AM, it had traveled for exactly one hour, so it had traveled 20 km.
At 8 AM, the distance between the two trains is 110 - 20 km or 90 km.
Let’s work in the frame of reference of train A. For someone on train A, train B is traveling towards it with a speed of 20 + 25 km/hr or 45 km/hr. (They are moving towards each other).
The distance between the two trains at 8 AM is 90 km.
So the time taken by train B to travel to train A would be 90 km / 45 km/hr
which is 2 hours.
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