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Certainly! Let's break down the problem.
Given:
(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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