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2 kg ki ek vastu saral Rekha ke anudish veg v=x3/2 se gatishil h parinami Bal davara vastu ko x=0 se x=4m tk visthapit krne me kiya gya work kya hoga?
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2 kg ki ek vastu saral Rekha ke anudish veg v=x3/2 se gatishil h parin...
Introduction
To find the work done on a 2 kg object moving along a straight line under the influence of a velocity defined by \( v = x^{3/2} \), we will follow these steps:
1. Determine the expression for acceleration
- The velocity \( v \) can be differentiated to find acceleration \( a \).
- \( v = x^{3/2} \)
- Therefore, \( a = \frac{dv}{dt} = \frac{dv}{dx} \cdot \frac{dx}{dt} = \frac{d(x^{3/2})}{dx} \cdot v = \frac{3}{2} x^{1/2} \cdot x^{3/2} = \frac{3}{2} x^2 \)
2. Calculate the force acting on the object
- Using Newton's second law \( F = ma \):
- \( F = 2 \, kg \cdot \frac{3}{2} x^2 = 3x^2 \, N \)
3. Compute the work done
- Work done \( W \) is defined as the integral of force over displacement:
\[
W = \int_{0}^{4} F \, dx = \int_{0}^{4} 3x^2 \, dx
\]
- Evaluating the integral:
\[
W = 3 \left[ \frac{x^3}{3} \right]_{0}^{4} = 3 \left[ \frac{4^3}{3} - 0 \right] = 3 \left[ \frac{64}{3} \right] = 64 \, J
\]
Conclusion
The total work done in moving the object from \( x = 0 \) to \( x = 4 \, m \) is \( 64 \, J \). This calculation illustrates how the force depends on the position of the object, affecting the work done in the process.
To find the work done on a 2 kg object moving along a straight line under the influence of a velocity defined by \( v = x^{3/2} \), we will follow these steps:
1. Determine the expression for acceleration
- The velocity \( v \) can be differentiated to find acceleration \( a \).
- \( v = x^{3/2} \)
- Therefore, \( a = \frac{dv}{dt} = \frac{dv}{dx} \cdot \frac{dx}{dt} = \frac{d(x^{3/2})}{dx} \cdot v = \frac{3}{2} x^{1/2} \cdot x^{3/2} = \frac{3}{2} x^2 \)
2. Calculate the force acting on the object
- Using Newton's second law \( F = ma \):
- \( F = 2 \, kg \cdot \frac{3}{2} x^2 = 3x^2 \, N \)
3. Compute the work done
- Work done \( W \) is defined as the integral of force over displacement:
\[
W = \int_{0}^{4} F \, dx = \int_{0}^{4} 3x^2 \, dx
\]
- Evaluating the integral:
\[
W = 3 \left[ \frac{x^3}{3} \right]_{0}^{4} = 3 \left[ \frac{4^3}{3} - 0 \right] = 3 \left[ \frac{64}{3} \right] = 64 \, J
\]
Conclusion
The total work done in moving the object from \( x = 0 \) to \( x = 4 \, m \) is \( 64 \, J \). This calculation illustrates how the force depends on the position of the object, affecting the work done in the process.
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2 kg ki ek vastu saral Rekha ke anudish veg v=x3/2 se gatishil h parinami Bal davara vastu ko x=0 se x=4m tk visthapit krne me kiya gya work kya hoga?
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2 kg ki ek vastu saral Rekha ke anudish veg v=x3/2 se gatishil h parinami Bal davara vastu ko x=0 se x=4m tk visthapit krne me kiya gya work kya hoga? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 2 kg ki ek vastu saral Rekha ke anudish veg v=x3/2 se gatishil h parinami Bal davara vastu ko x=0 se x=4m tk visthapit krne me kiya gya work kya hoga? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2 kg ki ek vastu saral Rekha ke anudish veg v=x3/2 se gatishil h parinami Bal davara vastu ko x=0 se x=4m tk visthapit krne me kiya gya work kya hoga?.
2 kg ki ek vastu saral Rekha ke anudish veg v=x3/2 se gatishil h parinami Bal davara vastu ko x=0 se x=4m tk visthapit krne me kiya gya work kya hoga? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 2 kg ki ek vastu saral Rekha ke anudish veg v=x3/2 se gatishil h parinami Bal davara vastu ko x=0 se x=4m tk visthapit krne me kiya gya work kya hoga? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2 kg ki ek vastu saral Rekha ke anudish veg v=x3/2 se gatishil h parinami Bal davara vastu ko x=0 se x=4m tk visthapit krne me kiya gya work kya hoga?.
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