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Question

The distance between two places A and B is 180km by road and 120km by air. An airplane takes 20minto go from A to B whereas a deluxe bus starting at A takes 5h to reach B. Find the average speed and average velocity by both means of transport. (Ignore the vertical ascent of the airplane).


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Solution

Step 1: Given data

Distance traveled by deluxe bus, dr=180km.

Distance traveled by airplane, da=120km.

Time taken by airplane to travel between A and B, tr=20min=2060=13h.

Time is taken by deluxe bus to travel between A and B, ta=5h.

The diagrammatic representation of the given data is given below:

Step 2: Calculate the average speed of the bus and airplane

Distance:

  1. The complete length of the path between any two points.
  2. It is a scalar quantity as it only has magnitude.

Displacement:

  1. It is the shortest path between the initial and final positions.
  2. It is a vector quantity as it has both direction and magnitude.

The formula for average speed is Averagespeed=TotaldistanceTotaltime.

Therefore, the average speed of the bus is:

sr=1805=36kmh-1

Therefore, the average speed of the airplane is:

sa=12013=360kmh-1

Step 3: Calculate the average velocity of the bus and airplane

The formula for average velocity is Averagevelocity=TotaldisplacementTotaltime.

As both the airplane and bus are taking the shortest path to reach point B, their distances will be equal to their displacements.

Therefore, the average velocity of the bus is:

vr=1805=36kmh-1

Therefore, the average velocity of the airplane is:

va=12013=360kmh-1

Thus,

  1. The average speed of the bus is 36kmh-1 and its average velocity is 36kmh-1.
  2. The average speed of the airplane is 360kmh-1 and its average velocity is 360kmh-1.

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