The distance from Patna to Ranchi is 260 km by air and 320 km by road. An aeroplane requires 30 minutes to travel from Patna to Ranchi, while a delux bus takes 8 hours. Determine the average velocity of the bus.

Step-by-step solution

The average velocity is defined as the ratio of total displacement to the total time taken. The displacement of the bus is the shortest straight-line distance between the initial and final positions, which is equal to the distance by air. Displacement = 260 km The direction of displacement is from Patna to Ranchi. Time taken by the bus = 8 h Average velocity = Displacement Time = 260 8 = 32.5 km/h The direction of the average velocity is the same as the direction of displacement, which is from Patna to Ranchi.