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Work done by a one-dimensional variable force F(x) or F(y) between two positions

This type of question, asked 6 times: 2021 Paper 15, 1 Feb 2023, 11 Apr 2023, 15 Apr 2023, 9 Apr 2024, 24 Jan 2025. All 6 questions below, oldest first.

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  1. Question 1

    2021 Paper 15

    17
    A force (5y+4)j^(5y+ 4)\widehat{j} displaces a particle from y=0y = 0 to y=2y = 2. Find work done by force.

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  2. Question 2

    1 Feb 2023

    117
    A force F=(5+3y2)F =\left( 5 + 3y^{2} \right) acts on a particle in the yy-direction, where FF is in newton and yy is in meter. The work done by the force during a displacement from y=2 my = 2\text{ }m to y=5 my = 5\text{ }m is ____J.

  3. Question 3

    11 Apr 2023

    24
    A force F→=(2+3x)i^\overrightarrow{F}= (2 + 3x)\widehat{i} acts on a particle in the xx direction where FF is in newton and xx is in meter. The work done by this force during a displacement from x=0x = 0 to x=4 mx = 4\text{ }m, is ____\_\_\_\_ J.

  4. Question 4

    15 Apr 2023

    29
    A block of mass 10 kg10\text{ }kg is moving along xx-axis under the action of force F=5xNF = 5xN. The work done by the force in moving the block from x=2 mx = 2\text{ }m to 4 m4\text{ }m will be___ J.

  5. Question 5

    9 Apr 2024

    119
    A force (3x2+2x−5)N\left( 3x^{2}+ 2x- 5 \right)N displaces a body from x=2 mx = 2\text{ }m to x=4 mx = 4\text{ }m. Work done by this force is ______ JJ.

  6. Question 6

    24 Jan 2025

    19
    A force F=α+βx2F = \alpha + \beta x^{2} acts on an object in the x -direction. The work done by the force is 5 J when the object is displaced by 1 m . If the constant, α=1 N\alpha = 1\text{ }N then β\beta will be

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