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PhysicsNEET 2025Relative velocity in one dimension

Motion in a Straight Line

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every TT min. A girl driving a scooty at a speed of 60 km/h in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period TT of the bus service and the speed (assumed constant) of the buses.

  1. A.9 min, 40 km/h
  2. B.25 min, 100 km/h
  3. C.10 min, 90 km/h
  4. D.15 min, 120 km/h✓

Solution

Let bus speed be vv. Same direction: buses catch her every 30 min, so vTv−60=30\frac{vT}{v - 60} = 30; opposite: vTv+60=10\frac{vT}{v + 60} = 10. Dividing, v+60v−60=3⇒v=120\frac{v + 60}{v - 60} = 3 \Rightarrow v = 120 km/h, then T=30×60120=15T = \frac{30 \times 60}{120} = 15 min.

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