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The acceleration of the particle moving in a straight line(x axis) is given by a =4t - 30 where a is metre per second square and t is second the initial position at t =0 is x not equal to 50 m and the initial velocity v not equal to 3 metre per second find the distance in metre of the particle from the origin at equal to 3 second?
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The acceleration of the particle moving in a straight line(x axis) is ...
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The acceleration of the particle moving in a straight line(x axis) is ...
Calculating Distance of the Particle at t = 3 seconds
- Given:
- Acceleration (a) = 4t - 30
- Initial position (x₀) = 50 m
- Initial velocity (v₀) = 3 m/s
- Formula:
- Velocity (v) = ∫(4t - 30) dt
- Position (x) = ∫v dt
- Calculating Velocity:
- v = ∫(4t - 30) dt
- v = 2t² - 30t + C (integrating with respect to time)
- Applying initial velocity condition: v₀ = 3
- 3 = 2(0)² - 30(0) + C
- C = 3
- Calculating Position:
- x = ∫v dt
- x = ∫(2t² - 30t + 3) dt
- x = (2/3)t³ - 15t² + 3t + D (integrating with respect to time)
- Applying initial position condition: x₀ = 50
- 50 = (2/3)(0)³ - 15(0)² + 3(0) + D
- D = 50
- Distance of Particle at t = 3 seconds:
- x = (2/3)(3)³ - 15(3)² + 3(3) + 50
- x = 18 - 135 + 9 + 50
- x = -108 + 59
- x = -49 m
Therefore, the distance of the particle from the origin at t = 3 seconds is 49 meters.
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The acceleration of the particle moving in a straight line(x axis) is given by a =4t - 30 where a is metre per second square and t is second the initial position at t =0 is x not equal to 50 m and the initial velocity v not equal to 3 metre per second find the distance in metre of the particle from the origin at equal to 3 second?
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The acceleration of the particle moving in a straight line(x axis) is given by a =4t - 30 where a is metre per second square and t is second the initial position at t =0 is x not equal to 50 m and the initial velocity v not equal to 3 metre per second find the distance in metre of the particle from the origin at equal to 3 second? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The acceleration of the particle moving in a straight line(x axis) is given by a =4t - 30 where a is metre per second square and t is second the initial position at t =0 is x not equal to 50 m and the initial velocity v not equal to 3 metre per second find the distance in metre of the particle from the origin at equal to 3 second? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The acceleration of the particle moving in a straight line(x axis) is given by a =4t - 30 where a is metre per second square and t is second the initial position at t =0 is x not equal to 50 m and the initial velocity v not equal to 3 metre per second find the distance in metre of the particle from the origin at equal to 3 second?.
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