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If a car with acceleration dependent on displacement as a=6x^2 2x 5m/s^2 find the velocity of the particle ,when it is at x=3 metre ,given that ,initially it starts from x=1 with velocity 2m/s ?
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If a car with acceleration dependent on displacement as a=6x^2 2x 5m/s...
Problem Statement
A car has an acceleration function a=6x^2+2x+5m/s^2, where x is the displacement. If the car starts from x=1 with a velocity of 2m/s, what is its velocity when it reaches x=3m?
Solution
- Integrate the acceleration function to get the velocity function
- Find the velocity at x=3m
- Answer
We can integrate the acceleration function to get the velocity function:
v = ∫(6x^2+2x+5)dx = 2x^3 + x^2 + 5x + C
where C is the constant of integration. To find C, we use the initial conditions:
v(1) = 2m/s
2 = 2(1)^3 + (1)^2 + 5(1) + C
C = -5
Therefore, the velocity function is:
v = 2x^3 + x^2 + 5x - 5
To find the velocity when x=3m, we simply plug in x=3 into the velocity function:
v(3) = 2(3)^3 + (3)^2 + 5(3) - 5 = 71m/s
The velocity of the car when it reaches x=3m is 71m/s.
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If a car with acceleration dependent on displacement as a=6x^2 2x 5m/s^2 find the velocity of the particle ,when it is at x=3 metre ,given that ,initially it starts from x=1 with velocity 2m/s ?
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If a car with acceleration dependent on displacement as a=6x^2 2x 5m/s^2 find the velocity of the particle ,when it is at x=3 metre ,given that ,initially it starts from x=1 with velocity 2m/s ? 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 If a car with acceleration dependent on displacement as a=6x^2 2x 5m/s^2 find the velocity of the particle ,when it is at x=3 metre ,given that ,initially it starts from x=1 with velocity 2m/s ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a car with acceleration dependent on displacement as a=6x^2 2x 5m/s^2 find the velocity of the particle ,when it is at x=3 metre ,given that ,initially it starts from x=1 with velocity 2m/s ?.
If a car with acceleration dependent on displacement as a=6x^2 2x 5m/s^2 find the velocity of the particle ,when it is at x=3 metre ,given that ,initially it starts from x=1 with velocity 2m/s ? 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 If a car with acceleration dependent on displacement as a=6x^2 2x 5m/s^2 find the velocity of the particle ,when it is at x=3 metre ,given that ,initially it starts from x=1 with velocity 2m/s ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a car with acceleration dependent on displacement as a=6x^2 2x 5m/s^2 find the velocity of the particle ,when it is at x=3 metre ,given that ,initially it starts from x=1 with velocity 2m/s ?.
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