QuestionDecember 18, 2025

18. A force F(x)=10x(inN) acts over a displacement from x=0 to x=3 m. What is the work done?

18. A force F(x)=10x(inN) acts over a displacement from x=0 to x=3 m. What is the work done?
18. A force F(x)=10x(inN) acts over a displacement from x=0 to x=3 m. What is the work done?

Solution
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Answer

45 J Explanation 1. Write the Work Formula for Variable Force Work done by a variable force: W = \int_{x_1}^{x_2} F(x)\,dx 2. Substitute the Given Force and Limits F(x) = 10x, limits: x_1=0, x_2=3 3. Integrate and Calculate W = \int_{0}^{3} 10x\,dx = 10\int_{0}^{3} x\,dx = 10\left[\frac{x^2}{2}\right]_0^3 = 10 \times \frac{9}{2} = 45

Explanation

1. Write the Work Formula for Variable Force<br /> Work done by a variable force: $W = \int_{x_1}^{x_2} F(x)\,dx$<br />2. Substitute the Given Force and Limits<br /> $F(x) = 10x$, limits: $x_1=0$, $x_2=3$<br />3. Integrate and Calculate<br /> $W = \int_{0}^{3} 10x\,dx = 10\int_{0}^{3} x\,dx = 10\left[\frac{x^2}{2}\right]_0^3 = 10 \times \frac{9}{2} = 45$
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