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Acceleration (or force) when velocity is given as a function of position

This type of question, asked 5 times: 2021 Paper 20, 25 Jul 2022, 11 Apr 2023, 1 Feb 2024, 7 Apr 2025. All 5 questions below, oldest first.

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  1. Question 1

    2021 Paper 20

    27
    If the velocity of a body related to displacement xx is given by v=5000+24x m/sv =\sqrt{5000 + 24x}\text{ }m/s, then the acceleration of the body is ..... m/s2m/s^{2}.

  2. Question 2

    25 Jul 2022

    111
    A particle is moving in a straight line such that its velocity is increasing at 5 ms−15{\text{ }ms}^{- 1} per meter. The acceleration of the particle is ____\_\_\_\_ ms−2ms^{- 2} at a point where its velocity is 20 ms−120{\text{ }ms}^{- 1}

  3. Question 3

    11 Apr 2023

    98
    A body of mass 500 g500\text{ }g moves along xx-axis such that it's velocity varies with displacement xx according to the relation v=10x m/sv = 10\sqrt{x}\text{ }m/s the force acting on the body is:-

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  4. Question 4

    1 Feb 2024

    112
    A particle initially at rest starts moving from reference point. x=0x = 0 along xx-axis, with velocity vv that varies as v=4xm/sv = 4\sqrt{x}m/s. The acceleration of the particle is _______ ms−2ms^{- 2}.

  5. Question 5

    7 Apr 2025

    94
    An object with mass 500 g moves along x -axis with speed v=4x m/sv = 4\sqrt{x}\text{ }m/s. The force acting on the object is :

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