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A particle moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 m/s, find average acceleration of particle from t = 0,to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20?
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A particle moves along x-axis with acceleration a = 6(t− 1), where t i...
- **Initial Conditions**
Given:
- Initial velocity, Vo = 2 m/s
- Initial position, x = 0
- **Acceleration Function**
The acceleration of the particle is given as a = 6(t - 1) m/s^2.
- **Average Acceleration**
To find the average acceleration of the particle from t = 0 to t = 10 seconds, we can use the formula:
\[Average\:Acceleration = \frac{Change\:in\:Velocity}{Time\:Interval}\]
- **Change in Velocity**
The change in velocity can be calculated by integrating the acceleration function with respect to time:
\[Change\:in\:Velocity = \int_{0}^{10} 6(t - 1) dt\]
\[Change\:in\:Velocity = \left[3t^2 - 6t\right]_{0}^{10}\]
\[Change\:in\:Velocity = 300\]
- **Time Interval**
The time interval is given as 10 seconds.
- **Average Acceleration Calculation**
Substitute the values into the formula:
\[Average\:Acceleration = \frac{300}{10}\]
\[Average\:Acceleration = 30\:m/s^2\]
Therefore, the average acceleration of the particle from t = 0 to t = 10 seconds is 30 m/s^2. Hence, the correct answer is (a) 30.
Given:
- Initial velocity, Vo = 2 m/s
- Initial position, x = 0
- **Acceleration Function**
The acceleration of the particle is given as a = 6(t - 1) m/s^2.
- **Average Acceleration**
To find the average acceleration of the particle from t = 0 to t = 10 seconds, we can use the formula:
\[Average\:Acceleration = \frac{Change\:in\:Velocity}{Time\:Interval}\]
- **Change in Velocity**
The change in velocity can be calculated by integrating the acceleration function with respect to time:
\[Change\:in\:Velocity = \int_{0}^{10} 6(t - 1) dt\]
\[Change\:in\:Velocity = \left[3t^2 - 6t\right]_{0}^{10}\]
\[Change\:in\:Velocity = 300\]
- **Time Interval**
The time interval is given as 10 seconds.
- **Average Acceleration Calculation**
Substitute the values into the formula:
\[Average\:Acceleration = \frac{300}{10}\]
\[Average\:Acceleration = 30\:m/s^2\]
Therefore, the average acceleration of the particle from t = 0 to t = 10 seconds is 30 m/s^2. Hence, the correct answer is (a) 30.
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A particle moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 m/s, find average acceleration of particle from t = 0,to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20?
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A particle moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 m/s, find average acceleration of particle from t = 0,to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20? 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 moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 m/s, find average acceleration of particle from t = 0,to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 m/s, find average acceleration of particle from t = 0,to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20?.
A particle moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 m/s, find average acceleration of particle from t = 0,to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20? 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 moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 m/s, find average acceleration of particle from t = 0,to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 m/s, find average acceleration of particle from t = 0,to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20?.
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