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The position x of a particle along a straight line is given as x= 3t2-18t. the maximum speed in the time interval t=0 to t=2 is? plz give the solution of the above que..
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The position x of a particle along a straight line is given as x= 3t2-...
Maximum Speed Calculation:
- To find the maximum speed of the particle, we need to determine the velocity of the particle first.
- Velocity can be calculated by taking the derivative of the position function with respect to time.
- Given x = 3t^2 - 18t, the velocity function v(t) is obtained by taking the derivative of x with respect to t.
- v(t) = dx/dt = d(3t^2 - 18t)/dt = 6t - 18.
Finding the Maximum Speed:
- To find the maximum speed, we need to find the critical points of the velocity function.
- Setting v(t) = 0, we get 6t - 18 = 0 which gives t = 3 as the critical point.
- We also need to check the endpoints of the interval t=0 and t=2.
- Calculating v(0) = 6(0) - 18 = -18 and v(2) = 6(2) - 18 = 0.
Determining Maximum Speed:
- The speed of the particle is given by the absolute value of the velocity, so we consider |v(t)|.
- Calculate |v(0)| = |-18| = 18, |v(2)| = |0| = 0, and |v(3)| = |6(3) - 18| = 0.
- The maximum speed in the interval t=0 to t=2 is the maximum value obtained from the absolute values of the velocity function.
- Therefore, the maximum speed is 18 units, achieved at t=0.
- To find the maximum speed of the particle, we need to determine the velocity of the particle first.
- Velocity can be calculated by taking the derivative of the position function with respect to time.
- Given x = 3t^2 - 18t, the velocity function v(t) is obtained by taking the derivative of x with respect to t.
- v(t) = dx/dt = d(3t^2 - 18t)/dt = 6t - 18.
Finding the Maximum Speed:
- To find the maximum speed, we need to find the critical points of the velocity function.
- Setting v(t) = 0, we get 6t - 18 = 0 which gives t = 3 as the critical point.
- We also need to check the endpoints of the interval t=0 and t=2.
- Calculating v(0) = 6(0) - 18 = -18 and v(2) = 6(2) - 18 = 0.
Determining Maximum Speed:
- The speed of the particle is given by the absolute value of the velocity, so we consider |v(t)|.
- Calculate |v(0)| = |-18| = 18, |v(2)| = |0| = 0, and |v(3)| = |6(3) - 18| = 0.
- The maximum speed in the interval t=0 to t=2 is the maximum value obtained from the absolute values of the velocity function.
- Therefore, the maximum speed is 18 units, achieved at t=0.
Community Answer
The position x of a particle along a straight line is given as x= 3t2-...
18 m/s can u plz answer whether it is correct or not..
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The position x of a particle along a straight line is given as x= 3t2-18t. the maximum speed in the time interval t=0 to t=2 is? plz give the solution of the above que..
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The position x of a particle along a straight line is given as x= 3t2-18t. the maximum speed in the time interval t=0 to t=2 is? plz give the solution of the above que.. for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The position x of a particle along a straight line is given as x= 3t2-18t. the maximum speed in the time interval t=0 to t=2 is? plz give the solution of the above que.. covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The position x of a particle along a straight line is given as x= 3t2-18t. the maximum speed in the time interval t=0 to t=2 is? plz give the solution of the above que...
The position x of a particle along a straight line is given as x= 3t2-18t. the maximum speed in the time interval t=0 to t=2 is? plz give the solution of the above que.. for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The position x of a particle along a straight line is given as x= 3t2-18t. the maximum speed in the time interval t=0 to t=2 is? plz give the solution of the above que.. covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The position x of a particle along a straight line is given as x= 3t2-18t. the maximum speed in the time interval t=0 to t=2 is? plz give the solution of the above que...
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