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A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km h-1 .Finding the market closed, he instantly turns and walks back home with a speed of 7.5 km h-1 What is the (a)Magnitude of average velocity, and (b)Average speed of the man over the interval of time (i) 0 to 30 min. (ii) 0 to 50 min. (iii) 0 to 40 min? [Note: You will appreciate from this exercise why it is better to define average speed as total path length divided by time, and not as magnitude of average velocity. You would not like to tell the tired man on his return home that his average speed was zero!]

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Certainly! Let's break down the problem. Given: Distance to market = 2.5 km Speed to market = 5 km/h Speed returning home = 7.5 km/h (a) Magnitude of average velocity: Average velocity is the total displacement divided by the total time taken. Total displacement = 0 km (since he returns home) Total...
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Certainly! Let's break down the problem.

Given:

  • Distance to market = 2.5 km
  • Speed to market = 5 km/h
  • Speed returning home = 7.5 km/h

(a) Magnitude of average velocity: Average velocity is the total displacement divided by the total time taken.

Total displacement = 0 km (since he returns home) Total time taken = Time to reach market + Time to return home

Time to reach market = Distance / Speed = 2.5 km / 5 km/h = 0.5 hours Time to return home = Distance / Speed = 2.5 km / 7.5 km/h = 1/3 hours

Total time taken = 0.5 hours + 1/3 hours = 5/6 hours

Average velocity = Total displacement / Total time taken = 0 km / (5/6) hours = 0 km/h

(b) Average speed: Average speed is the total distance traveled divided by the total time taken.

(i) 0 to 30 min (0.5 hours): Total distance traveled = 2.5 km (to market) + 2.5 km (returning home) = 5 km Average speed = Total distance / Total time = 5 km / 0.5 hours = 10 km/h

(ii) 0 to 50 min (5/6 hours): Total distance traveled remains the same (5 km) Average speed = Total distance / Total time = 5 km / (5/6) hours = 6 km/h

(iii) 0 to 40 min (2/3 hours): Total distance traveled = 2.5 km (to market) + 2.5 km (returning home) = 5 km Average speed = Total distance / Total time = 5 km / (2/3) hours = 7.5 km/h

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