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A particle is starting from rest has an acceleration that increases linearly with time as a equal to 2T then the distance travelled in 3rd second will be?
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A particle is starting from rest has an acceleration that increases li...
To find the distance travelled by a particle in the 3rd second, we need to analyze its motion given that the acceleration increases linearly with time.
Understanding Acceleration
- The acceleration, a, is defined as a = 2T, where T is time in seconds.
- This means at T = 1s, a = 2 m/s²; at T = 2s, a = 4 m/s²; and at T = 3s, a = 6 m/s².
Finding Velocity
- To find velocity, we integrate acceleration with respect to time.
- The velocity at time T can be determined using the formula:
v(T) = ∫ a dt = ∫ 2T dt = T² + C (where C = initial velocity, which is 0 since the particle starts from rest).
- Thus, v(T) = T².
Finding Distance
- The distance travelled in the nth second can be calculated using the formula:
S(n) = v(n) - v(n-1).
- Now, we calculate the velocities:
- v(3) = 3² = 9 m/s
- v(2) = 2² = 4 m/s
- Therefore, the distance travelled in the 3rd second is:
S(3) = v(3) - v(2) = 9 m/s - 4 m/s = 5 m.
Conclusion
- The distance travelled by the particle in the 3rd second is 5 meters.
This calculation shows how the increasing acceleration affects the displacement over time.
Understanding Acceleration
- The acceleration, a, is defined as a = 2T, where T is time in seconds.
- This means at T = 1s, a = 2 m/s²; at T = 2s, a = 4 m/s²; and at T = 3s, a = 6 m/s².
Finding Velocity
- To find velocity, we integrate acceleration with respect to time.
- The velocity at time T can be determined using the formula:
v(T) = ∫ a dt = ∫ 2T dt = T² + C (where C = initial velocity, which is 0 since the particle starts from rest).
- Thus, v(T) = T².
Finding Distance
- The distance travelled in the nth second can be calculated using the formula:
S(n) = v(n) - v(n-1).
- Now, we calculate the velocities:
- v(3) = 3² = 9 m/s
- v(2) = 2² = 4 m/s
- Therefore, the distance travelled in the 3rd second is:
S(3) = v(3) - v(2) = 9 m/s - 4 m/s = 5 m.
Conclusion
- The distance travelled by the particle in the 3rd second is 5 meters.
This calculation shows how the increasing acceleration affects the displacement over time.
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A particle is starting from rest has an acceleration that increases linearly with time as a equal to 2T then the distance travelled in 3rd second will be?
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A particle is starting from rest has an acceleration that increases linearly with time as a equal to 2T then the distance travelled in 3rd second will be? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A particle is starting from rest has an acceleration that increases linearly with time as a equal to 2T then the distance travelled in 3rd second will be? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is starting from rest has an acceleration that increases linearly with time as a equal to 2T then the distance travelled in 3rd second will be?.
A particle is starting from rest has an acceleration that increases linearly with time as a equal to 2T then the distance travelled in 3rd second will be? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A particle is starting from rest has an acceleration that increases linearly with time as a equal to 2T then the distance travelled in 3rd second will be? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is starting from rest has an acceleration that increases linearly with time as a equal to 2T then the distance travelled in 3rd second will be?.
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