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A particle moves in a circular path of radius 1 metre with uniform speed and takes 4 seconds to complete the circular path . Find distance displacement and average speed and average velocity for : A to B , Ato C , Ato D and A to A?
Most Upvoted Answer
A particle moves in a circular path of radius 1 metre with uniform spe...
Given data:
- Radius of circular path = 1 metre
- Time taken to complete circular path = 4 seconds
To solve this problem, we can use the following concepts:
- Distance traveled = Circumference of circular path
- Displacement = Straight line distance between initial and final points
- Average speed = Total distance traveled / Total time taken
- Average velocity = Displacement / Total time taken
Now, let's find the distance, displacement, average speed and average velocity for each case:
A to B:
- Distance traveled = Circumference of circle = 2πr = 2π(1) = 2π metres
- Displacement = Straight line distance between A and B = r = 1 metre
- Total time taken = 4 seconds
- Average speed = Total distance traveled / Total time taken = 2π / 4 = π/2 metres per second
- Average velocity = Displacement / Total time taken = 1 / 4 = 0.25 metres per second
A to C:
- Distance traveled = Half circumference of circle = πr = π(1) = π metres
- Displacement = Straight line distance between A and C = 2r = 2 metres
- Total time taken = 2 seconds (half of the time taken to complete the circle)
- Average speed = Total distance traveled / Total time taken = π / 2 = 1.57 metres per second
- Average velocity = Displacement / Total time taken = 2 / 2 = 1 metre per second
A to D:
- Distance traveled = Three-fourth circumference of circle = 3πr/2 = 3π/2 metres
- Displacement = Straight line distance between A and D = 0 (since D is the starting point)
- Total time taken = 3 seconds (three-fourth of the time taken to complete the circle)
- Average speed = Total distance traveled / Total time taken = 3π/2 / 3 = π/2 metres per second
- Average velocity = Displacement / Total time taken = 0 / 3 = 0 metres per second
A to A:
- Distance traveled = Full circumference of circle = 2πr = 2π metres
- Displacement = Straight line distance between A and A = 0 (since A is the starting and ending point)
- Total time taken = 4 seconds
- Average speed = Total distance traveled / Total time taken = 2π / 4 = π/2 metres per second
- Average velocity = Displacement / Total time taken = 0 / 4 = 0 metres per second
Therefore, the answers are:
- A to B: Distance = 2π metres, Displacement = 1 metre, Average speed = π/2 metres per second, Average velocity = 0.25 metres per second
- A to C: Distance = π metres, Displacement = 2 metres, Average speed = 1.57 metres per second, Average velocity = 1 metre per second
- A to D: Distance = 3π/2 metres, Displacement = 0 metres, Average speed = π/2 metres per second, Average velocity = 0 metres per second
- A to A: Distance = 2π metres, Displacement = 0 metres, Average speed = π/2 metres
- Radius of circular path = 1 metre
- Time taken to complete circular path = 4 seconds
To solve this problem, we can use the following concepts:
- Distance traveled = Circumference of circular path
- Displacement = Straight line distance between initial and final points
- Average speed = Total distance traveled / Total time taken
- Average velocity = Displacement / Total time taken
Now, let's find the distance, displacement, average speed and average velocity for each case:
A to B:
- Distance traveled = Circumference of circle = 2πr = 2π(1) = 2π metres
- Displacement = Straight line distance between A and B = r = 1 metre
- Total time taken = 4 seconds
- Average speed = Total distance traveled / Total time taken = 2π / 4 = π/2 metres per second
- Average velocity = Displacement / Total time taken = 1 / 4 = 0.25 metres per second
A to C:
- Distance traveled = Half circumference of circle = πr = π(1) = π metres
- Displacement = Straight line distance between A and C = 2r = 2 metres
- Total time taken = 2 seconds (half of the time taken to complete the circle)
- Average speed = Total distance traveled / Total time taken = π / 2 = 1.57 metres per second
- Average velocity = Displacement / Total time taken = 2 / 2 = 1 metre per second
A to D:
- Distance traveled = Three-fourth circumference of circle = 3πr/2 = 3π/2 metres
- Displacement = Straight line distance between A and D = 0 (since D is the starting point)
- Total time taken = 3 seconds (three-fourth of the time taken to complete the circle)
- Average speed = Total distance traveled / Total time taken = 3π/2 / 3 = π/2 metres per second
- Average velocity = Displacement / Total time taken = 0 / 3 = 0 metres per second
A to A:
- Distance traveled = Full circumference of circle = 2πr = 2π metres
- Displacement = Straight line distance between A and A = 0 (since A is the starting and ending point)
- Total time taken = 4 seconds
- Average speed = Total distance traveled / Total time taken = 2π / 4 = π/2 metres per second
- Average velocity = Displacement / Total time taken = 0 / 4 = 0 metres per second
Therefore, the answers are:
- A to B: Distance = 2π metres, Displacement = 1 metre, Average speed = π/2 metres per second, Average velocity = 0.25 metres per second
- A to C: Distance = π metres, Displacement = 2 metres, Average speed = 1.57 metres per second, Average velocity = 1 metre per second
- A to D: Distance = 3π/2 metres, Displacement = 0 metres, Average speed = π/2 metres per second, Average velocity = 0 metres per second
- A to A: Distance = 2π metres, Displacement = 0 metres, Average speed = π/2 metres
Community Answer
A particle moves in a circular path of radius 1 metre with uniform spe...
Mate , where the other points are located is necessary to answer your question Eg : where does point B lies is necessary to answer the distance between A to B.
But ,
from your given information I
can only answer these :
* Displacement between A to A = 0
* Average speed from A to A = 2πr÷time taken
= 2×3.14×1÷4
=6.28÷4
=1.57m/s
But ,
from your given information I
can only answer these :
* Displacement between A to A = 0
* Average speed from A to A = 2πr÷time taken
= 2×3.14×1÷4
=6.28÷4
=1.57m/s
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A particle moves in a circular path of radius 1 metre with uniform speed and takes 4 seconds to complete the circular path . Find distance displacement and average speed and average velocity for : A to B , Ato C , Ato D and A to A?
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