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The displacement x of a particle moving along x-axis at time t is given by x² = 2t² + 6t. The velocity at any time t is?
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The displacement x of a particle moving along x-axis at time t is give...
Understanding the Displacement Equation
The displacement of the particle is given by the equation:
x² = 2t² + 6t
This can be interpreted as a relationship between the displacement (x) and time (t).
Finding Velocity
Velocity is defined as the rate of change of displacement with respect to time. To find the velocity, we first need to differentiate the displacement equation with respect to time.
Step 1: Differentiate the Displacement Equation
Using implicit differentiation on the equation x² = 2t² + 6t:
- Differentiate both sides:
d/dt(x²) = d/dt(2t² + 6t)
- Applying the chain rule:
2x(dx/dt) = 4t + 6
Here, dx/dt is the velocity (v).
Step 2: Solve for Velocity
Now, we rearrange the equation to isolate dx/dt (velocity):
dx/dt = (4t + 6)/(2x)
Step 3: Express x in Terms of t
To express velocity in a more usable form, we can substitute x from the original equation:
x = √(2t² + 6t)
Now substituting this into the velocity equation:
dx/dt = (4t + 6)/(2√(2t² + 6t))
Final Expression for Velocity
Thus, the velocity at any time t is given by:
v(t) = (4t + 6)/(2√(2t² + 6t))
This expression allows us to calculate the velocity of the particle at any specific time.
The displacement of the particle is given by the equation:
x² = 2t² + 6t
This can be interpreted as a relationship between the displacement (x) and time (t).
Finding Velocity
Velocity is defined as the rate of change of displacement with respect to time. To find the velocity, we first need to differentiate the displacement equation with respect to time.
Step 1: Differentiate the Displacement Equation
Using implicit differentiation on the equation x² = 2t² + 6t:
- Differentiate both sides:
d/dt(x²) = d/dt(2t² + 6t)
- Applying the chain rule:
2x(dx/dt) = 4t + 6
Here, dx/dt is the velocity (v).
Step 2: Solve for Velocity
Now, we rearrange the equation to isolate dx/dt (velocity):
dx/dt = (4t + 6)/(2x)
Step 3: Express x in Terms of t
To express velocity in a more usable form, we can substitute x from the original equation:
x = √(2t² + 6t)
Now substituting this into the velocity equation:
dx/dt = (4t + 6)/(2√(2t² + 6t))
Final Expression for Velocity
Thus, the velocity at any time t is given by:
v(t) = (4t + 6)/(2√(2t² + 6t))
This expression allows us to calculate the velocity of the particle at any specific time.
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The displacement x of a particle moving along x-axis at time t is given by x² = 2t² + 6t. The velocity at any time t is?
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The displacement x of a particle moving along x-axis at time t is given by x² = 2t² + 6t. The velocity at any time t is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The displacement x of a particle moving along x-axis at time t is given by x² = 2t² + 6t. The velocity at any time t is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The displacement x of a particle moving along x-axis at time t is given by x² = 2t² + 6t. The velocity at any time t is?.
The displacement x of a particle moving along x-axis at time t is given by x² = 2t² + 6t. The velocity at any time t is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The displacement x of a particle moving along x-axis at time t is given by x² = 2t² + 6t. The velocity at any time t is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The displacement x of a particle moving along x-axis at time t is given by x² = 2t² + 6t. The velocity at any time t is?.
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