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1. A person Travels along a straight road for half the distance with velocity V1 and remaining half distance with velocity V2 the average velocity is given by? Sol) 2V1V2/V1+V2?
Verified Answer
1. A person Travels along a straight road for half the distance with v...
Case I:
let x1 be the half distance covered.
speed=v1
time taken to cover the first half of the journey :
t1=distance/speed
=(x/2)/v1
Case II
let x2 be the half distance covered.
speed=v2
time taken to cover the second half of the journey :
t2=distance/speed
=(x/2)/v2
Total time=T=t1+t2
=x/(2v1)+x/(2v2)
T=x/2[1/v1+1/v2]
=x[v1+v2]/2v1v2
Average Velocity= Displacement/ total time
=x/x[v1+v2]/2v1v2
=2v1v2/(v1+v2)
∴Average velocity is given by 2v1v2/(v1+v2)
This question is part of UPSC exam. View all Class 11 courses
Most Upvoted Answer
1. A person Travels along a straight road for half the distance with v...
Explanation:
To find the average velocity, we need to calculate the total displacement and divide it by the total time taken.
Step 1: Calculate the total displacement:
Since the person is traveling along a straight road, the total displacement is the sum of the displacements covered in the first half and the second half of the journey.
Let the total distance be 'd'.
Displacement in the first half of the journey = d/2
Displacement in the second half of the journey = d/2
Therefore, the total displacement = (d/2) + (d/2) = d
Step 2: Calculate the total time taken:
To calculate the total time taken, we need to consider the individual times taken for each half of the journey.
Let the time taken for the first half of the journey be 't1' and the time taken for the second half of the journey be 't2'.
Since velocity = displacement/time, we can rearrange the formula as time = displacement/velocity.
Therefore,
Time taken for the first half of the journey (t1) = (d/2) / V1
Time taken for the second half of the journey (t2) = (d/2) / V2
The total time taken (T) = t1 + t2 = (d/2) / V1 + (d/2) / V2
Step 3: Calculate the average velocity:
The average velocity (Vavg) is given by the total displacement divided by the total time taken.
Therefore,
Average velocity (Vavg) = total displacement / total time taken
= d / T
= d / [(d/2) / V1 + (d/2) / V2]
Final Answer:
Hence, the average velocity is given by Vavg = 2V1V2 / (V1 + V2).
To find the average velocity, we need to calculate the total displacement and divide it by the total time taken.
Step 1: Calculate the total displacement:
Since the person is traveling along a straight road, the total displacement is the sum of the displacements covered in the first half and the second half of the journey.
Let the total distance be 'd'.
Displacement in the first half of the journey = d/2
Displacement in the second half of the journey = d/2
Therefore, the total displacement = (d/2) + (d/2) = d
Step 2: Calculate the total time taken:
To calculate the total time taken, we need to consider the individual times taken for each half of the journey.
Let the time taken for the first half of the journey be 't1' and the time taken for the second half of the journey be 't2'.
Since velocity = displacement/time, we can rearrange the formula as time = displacement/velocity.
Therefore,
Time taken for the first half of the journey (t1) = (d/2) / V1
Time taken for the second half of the journey (t2) = (d/2) / V2
The total time taken (T) = t1 + t2 = (d/2) / V1 + (d/2) / V2
Step 3: Calculate the average velocity:
The average velocity (Vavg) is given by the total displacement divided by the total time taken.
Therefore,
Average velocity (Vavg) = total displacement / total time taken
= d / T
= d / [(d/2) / V1 + (d/2) / V2]
Final Answer:
Hence, the average velocity is given by Vavg = 2V1V2 / (V1 + V2).
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1. A person Travels along a straight road for half the distance with velocity V1 and remaining half distance with velocity V2 the average velocity is given by? Sol) 2V1V2/V1+V2?
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1. A person Travels along a straight road for half the distance with velocity V1 and remaining half distance with velocity V2 the average velocity is given by? Sol) 2V1V2/V1+V2? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about 1. A person Travels along a straight road for half the distance with velocity V1 and remaining half distance with velocity V2 the average velocity is given by? Sol) 2V1V2/V1+V2? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1. A person Travels along a straight road for half the distance with velocity V1 and remaining half distance with velocity V2 the average velocity is given by? Sol) 2V1V2/V1+V2?.
1. A person Travels along a straight road for half the distance with velocity V1 and remaining half distance with velocity V2 the average velocity is given by? Sol) 2V1V2/V1+V2? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about 1. A person Travels along a straight road for half the distance with velocity V1 and remaining half distance with velocity V2 the average velocity is given by? Sol) 2V1V2/V1+V2? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1. A person Travels along a straight road for half the distance with velocity V1 and remaining half distance with velocity V2 the average velocity is given by? Sol) 2V1V2/V1+V2?.
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