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A body accelerates frim rest qith a uniform acceleration a for a time t. The uncertainity in a is 8% and the uncertainity in t us 40% .The uncertainity in the speed is?
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A body accelerates frim rest qith a uniform acceleration a for a time ...
Understanding the Problem
A body accelerates from rest with a uniform acceleration (a) for a time (t). We need to calculate the uncertainty in the final speed (v) based on the given uncertainties in acceleration and time.
Formula for Final Speed
- The final speed (v) can be expressed as:
v = a * t
Identifying the Uncertainties
- Uncertainty in acceleration (a): 8%
- Uncertainty in time (t): 40%
Calculating the Uncertainty in Speed
- To find the total uncertainty in speed (v), we use the formula for propagation of uncertainties:
Δv/v = Δa/a + Δt/t
- Where:
- Δv is the uncertainty in speed
- Δa is the uncertainty in acceleration
- Δt is the uncertainty in time
Substituting the Values
- Given:
- Δa/a = 8% = 0.08
- Δt/t = 40% = 0.40
- Therefore, the total relative uncertainty in speed (Δv/v):
Δv/v = 0.08 + 0.40 = 0.48
Final Calculation of Uncertainty
- To express this as a percentage, multiply by 100:
- Uncertainty in speed = 48%
Conclusion
In conclusion, the uncertainty in the speed of the body, given the uncertainties in acceleration and time, is 48%. This significant uncertainty highlights the impact of time measurement on the final speed when acceleration is not precisely known.
A body accelerates from rest with a uniform acceleration (a) for a time (t). We need to calculate the uncertainty in the final speed (v) based on the given uncertainties in acceleration and time.
Formula for Final Speed
- The final speed (v) can be expressed as:
v = a * t
Identifying the Uncertainties
- Uncertainty in acceleration (a): 8%
- Uncertainty in time (t): 40%
Calculating the Uncertainty in Speed
- To find the total uncertainty in speed (v), we use the formula for propagation of uncertainties:
Δv/v = Δa/a + Δt/t
- Where:
- Δv is the uncertainty in speed
- Δa is the uncertainty in acceleration
- Δt is the uncertainty in time
Substituting the Values
- Given:
- Δa/a = 8% = 0.08
- Δt/t = 40% = 0.40
- Therefore, the total relative uncertainty in speed (Δv/v):
Δv/v = 0.08 + 0.40 = 0.48
Final Calculation of Uncertainty
- To express this as a percentage, multiply by 100:
- Uncertainty in speed = 48%
Conclusion
In conclusion, the uncertainty in the speed of the body, given the uncertainties in acceleration and time, is 48%. This significant uncertainty highlights the impact of time measurement on the final speed when acceleration is not precisely known.
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A body accelerates frim rest qith a uniform acceleration a for a time t. The uncertainity in a is 8% and the uncertainity in t us 40% .The uncertainity in the speed is?
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A body accelerates frim rest qith a uniform acceleration a for a time t. The uncertainity in a is 8% and the uncertainity in t us 40% .The uncertainity in the speed is? 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 body accelerates frim rest qith a uniform acceleration a for a time t. The uncertainity in a is 8% and the uncertainity in t us 40% .The uncertainity in the speed is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body accelerates frim rest qith a uniform acceleration a for a time t. The uncertainity in a is 8% and the uncertainity in t us 40% .The uncertainity in the speed is?.
A body accelerates frim rest qith a uniform acceleration a for a time t. The uncertainity in a is 8% and the uncertainity in t us 40% .The uncertainity in the speed is? 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 body accelerates frim rest qith a uniform acceleration a for a time t. The uncertainity in a is 8% and the uncertainity in t us 40% .The uncertainity in the speed is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body accelerates frim rest qith a uniform acceleration a for a time t. The uncertainity in a is 8% and the uncertainity in t us 40% .The uncertainity in the speed is?.
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