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A circular cycle track has a circumference of 314m with AB as one of its diameter. A cyclist travels from A to B along the circular path with a constant magnitude 15.7m/s. Find distance travelled, displacement of cyclist if AB is in North -south direction and average velocity?
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A circular cycle track has a circumference of 314m with AB as one of i...
**Given:**
- Circumference of the cycle track = 314m
- Magnitude of velocity = 15.7m/s
**To find:**
- Distance traveled by the cyclist
- Displacement of the cyclist
- Average velocity
**Solution:**
**1. Distance traveled:**
Distance traveled by the cyclist is the total length of the circular path covered. Since the circumference of the cycle track is given, the distance traveled can be calculated using the formula:
Distance = Circumference of the track
Distance = 314m
Therefore, the distance traveled by the cyclist is 314m.
**2. Displacement:**
Displacement is the straight-line distance between the initial and final positions of the cyclist. In this case, the initial and final positions are points A and B, which lie on the diameter of the circle.
Since AB is a diameter, it is a straight line and its length is equal to the diameter of the circle.
Diameter = Circumference / π (pi)
Diameter = 314m / 3.14
Diameter ≈ 100m
Therefore, the displacement of the cyclist is 100m.
**3. Average velocity:**
Average velocity is the total displacement divided by the total time taken.
To calculate the average velocity, we need to know the time taken by the cyclist to travel from A to B. Since the magnitude of velocity is given as 15.7m/s, we can use the formula:
v = d / t
Where,
v = velocity (magnitude)
d = distance
t = time
Rearranging the formula, we get:
t = d / v
t = 100m / 15.7m/s
t ≈ 6.37s
Therefore, the time taken by the cyclist to travel from A to B is approximately 6.37 seconds.
Now, we can calculate the average velocity:
Average velocity = Displacement / Time
Average velocity = 100m / 6.37s
Average velocity ≈ 15.7 m/s
Therefore, the average velocity of the cyclist is approximately 15.7 m/s.
In summary:
- Distance traveled by the cyclist = 314m
- Displacement of the cyclist = 100m
- Average velocity of the cyclist = 15.7 m/s
- Circumference of the cycle track = 314m
- Magnitude of velocity = 15.7m/s
**To find:**
- Distance traveled by the cyclist
- Displacement of the cyclist
- Average velocity
**Solution:**
**1. Distance traveled:**
Distance traveled by the cyclist is the total length of the circular path covered. Since the circumference of the cycle track is given, the distance traveled can be calculated using the formula:
Distance = Circumference of the track
Distance = 314m
Therefore, the distance traveled by the cyclist is 314m.
**2. Displacement:**
Displacement is the straight-line distance between the initial and final positions of the cyclist. In this case, the initial and final positions are points A and B, which lie on the diameter of the circle.
Since AB is a diameter, it is a straight line and its length is equal to the diameter of the circle.
Diameter = Circumference / π (pi)
Diameter = 314m / 3.14
Diameter ≈ 100m
Therefore, the displacement of the cyclist is 100m.
**3. Average velocity:**
Average velocity is the total displacement divided by the total time taken.
To calculate the average velocity, we need to know the time taken by the cyclist to travel from A to B. Since the magnitude of velocity is given as 15.7m/s, we can use the formula:
v = d / t
Where,
v = velocity (magnitude)
d = distance
t = time
Rearranging the formula, we get:
t = d / v
t = 100m / 15.7m/s
t ≈ 6.37s
Therefore, the time taken by the cyclist to travel from A to B is approximately 6.37 seconds.
Now, we can calculate the average velocity:
Average velocity = Displacement / Time
Average velocity = 100m / 6.37s
Average velocity ≈ 15.7 m/s
Therefore, the average velocity of the cyclist is approximately 15.7 m/s.
In summary:
- Distance traveled by the cyclist = 314m
- Displacement of the cyclist = 100m
- Average velocity of the cyclist = 15.7 m/s
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A circular cycle track has a circumference of 314m with AB as one of its diameter. A cyclist travels from A to B along the circular path with a constant magnitude 15.7m/s. Find distance travelled, displacement of cyclist if AB is in North -south direction and average velocity?
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A circular cycle track has a circumference of 314m with AB as one of its diameter. A cyclist travels from A to B along the circular path with a constant magnitude 15.7m/s. Find distance travelled, displacement of cyclist if AB is in North -south direction and average velocity? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A circular cycle track has a circumference of 314m with AB as one of its diameter. A cyclist travels from A to B along the circular path with a constant magnitude 15.7m/s. Find distance travelled, displacement of cyclist if AB is in North -south direction and average velocity? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular cycle track has a circumference of 314m with AB as one of its diameter. A cyclist travels from A to B along the circular path with a constant magnitude 15.7m/s. Find distance travelled, displacement of cyclist if AB is in North -south direction and average velocity?.
A circular cycle track has a circumference of 314m with AB as one of its diameter. A cyclist travels from A to B along the circular path with a constant magnitude 15.7m/s. Find distance travelled, displacement of cyclist if AB is in North -south direction and average velocity? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A circular cycle track has a circumference of 314m with AB as one of its diameter. A cyclist travels from A to B along the circular path with a constant magnitude 15.7m/s. Find distance travelled, displacement of cyclist if AB is in North -south direction and average velocity? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular cycle track has a circumference of 314m with AB as one of its diameter. A cyclist travels from A to B along the circular path with a constant magnitude 15.7m/s. Find distance travelled, displacement of cyclist if AB is in North -south direction and average velocity?.
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