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A particle moves on a straightline in such a way that it covers 1st half distance with speed 3m/s and next half distance in two equal time intervals with speeds 4.5m/s and 7.5m/s respectively. Find average speed of the particle.
Most Upvoted Answer
A particle moves on a straightline in such a way that it covers 1st ha...
Given information:
- The particle covers the first half of the distance with a speed of 3 m/s.
- The second half of the distance is covered in two equal time intervals.
- The particle travels with speeds of 4.5 m/s and 7.5 m/s in these two time intervals respectively.
To find:
- The average speed of the particle.
Solution:
Step 1: Calculating time taken for each half of the distance
- Let's assume the total distance covered by the particle is 'd'.
- The first half of the distance is given by d/2.
- The time taken to cover the first half of the distance is given by (d/2) / 3 = d/6.
- The time taken to cover the second half of the distance is divided into two equal intervals.
- Let's assume the time taken for each interval is 't'.
- So, the total time taken for the second half of the distance is 2t.
Step 2: Calculating distance traveled in each interval
- The distance traveled in the first interval is given by 4.5t.
- The distance traveled in the second interval is given by 7.5t.
- The total distance traveled in the second half of the distance is (4.5t + 7.5t) = 12t.
Step 3: Equating distances in both halves
- The distance covered in the first half of the distance is d/2.
- The distance covered in the second half of the distance is 12t.
- Equating both distances, we get d/2 = 12t.
Step 4: Solving for time interval 't'
- From the above equation, we can solve for 't' as t = (d/2) / 12 = d/24.
Step 5: Calculating the average speed
- The total time taken to cover the entire distance is (d/6 + 2t).
- Substituting the value of 't', we get the total time taken as (d/6 + 2(d/24)) = (d/6 + d/12) = 3d/12 = d/4.
- The average speed is given by the total distance traveled divided by the total time taken.
- The total distance traveled is 'd'.
- The total time taken is d/4.
- Therefore, the average speed is d / (d/4) = 4 m/s.
Answer:
- The average speed of the particle is 4 m/s.
- The particle covers the first half of the distance with a speed of 3 m/s.
- The second half of the distance is covered in two equal time intervals.
- The particle travels with speeds of 4.5 m/s and 7.5 m/s in these two time intervals respectively.
To find:
- The average speed of the particle.
Solution:
Step 1: Calculating time taken for each half of the distance
- Let's assume the total distance covered by the particle is 'd'.
- The first half of the distance is given by d/2.
- The time taken to cover the first half of the distance is given by (d/2) / 3 = d/6.
- The time taken to cover the second half of the distance is divided into two equal intervals.
- Let's assume the time taken for each interval is 't'.
- So, the total time taken for the second half of the distance is 2t.
Step 2: Calculating distance traveled in each interval
- The distance traveled in the first interval is given by 4.5t.
- The distance traveled in the second interval is given by 7.5t.
- The total distance traveled in the second half of the distance is (4.5t + 7.5t) = 12t.
Step 3: Equating distances in both halves
- The distance covered in the first half of the distance is d/2.
- The distance covered in the second half of the distance is 12t.
- Equating both distances, we get d/2 = 12t.
Step 4: Solving for time interval 't'
- From the above equation, we can solve for 't' as t = (d/2) / 12 = d/24.
Step 5: Calculating the average speed
- The total time taken to cover the entire distance is (d/6 + 2t).
- Substituting the value of 't', we get the total time taken as (d/6 + 2(d/24)) = (d/6 + d/12) = 3d/12 = d/4.
- The average speed is given by the total distance traveled divided by the total time taken.
- The total distance traveled is 'd'.
- The total time taken is d/4.
- Therefore, the average speed is d / (d/4) = 4 m/s.
Answer:
- The average speed of the particle is 4 m/s.
Community Answer
A particle moves on a straightline in such a way that it covers 1st ha...
12 Firstly find average speed give with time and then use it with distance to calculate total
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A particle moves on a straightline in such a way that it covers 1st half distance with speed 3m/s and next half distance in two equal time intervals with speeds 4.5m/s and 7.5m/s respectively. Find average speed of the particle.
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A particle moves on a straightline in such a way that it covers 1st half distance with speed 3m/s and next half distance in two equal time intervals with speeds 4.5m/s and 7.5m/s respectively. Find average speed of the particle. 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 A particle moves on a straightline in such a way that it covers 1st half distance with speed 3m/s and next half distance in two equal time intervals with speeds 4.5m/s and 7.5m/s respectively. Find average speed of the particle. covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves on a straightline in such a way that it covers 1st half distance with speed 3m/s and next half distance in two equal time intervals with speeds 4.5m/s and 7.5m/s respectively. Find average speed of the particle..
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