A person goes from his home to market. For half of the total distance covered his speed is 6 km/hr. For the remaining half of the journey, his speed is 12 km/hr. What is the average speed of the person over complete journey? Does it matter if the person goes in a straight line or not? Will it matter if you are finding average velocity
Answers
Explanation :
Person goes from home to market. Speed of first half journey is 6 km/h. Speed of second half of journey is 12 km/h.
What is average speed of whole journey?
Let the distance of whole journey be s.
∴ Distance of first half = s/2
∴ Distance of second half = s/2
Formula to be used now :-
⇒ Speed = Distance/Time
⇒ 6 = (s/2)/Time
⇒ 6 × Time = s/2
⇒ Time = (s/2)/6
⇒ Time = (s/12) hours.
∴ Time taken to cross first half = (s/12) h
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For the second half of distance :-
⇒ 12 = (s/2)/Time
⇒ 12 × Time = s/2
⇒ Time = (s/2)/12
⇒ Time = (s/24) h
∴ Time taken to cross second half = (s/24) h
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Now using the formula of average speed :-
⇒ Av. speed = Total distance/Total time
⇒ Av. speed = s/(s/12 + s/24)
⇒ Av. speed = s/{(2s + s)/24}
⇒ Av. speed = s/(3s/34)
⇒ Av. speed = s × (24/3s)
⇒ Av. speed = 8 km/h
∴ Average speed of whole journey = 8 km/h
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No, it won't matter in this condition if person goes in straight line or not. As total distance will remain same.
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In this condition it won't matter if we are finding average velocity because person goes in straight line and person doesn't come back to its initial position.
[Note : If the person had come back to its initial position then average velocity would be 0. ]