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s = at^2 + bt + c with given displacement, velocity and acceleration: relation between a, b and c

The same question, asked 2 times: 15 May 2023 S2, 23 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    15 May 2023 S2

    129
    The equation of motion of a particle is s=at2+bt+cs = at^2+bt+c. If the displacement after 1 second is 20 m, velocity after 2 seconds is 30 m/sec and the acceleration is 10 m/sec2^2, then

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  2. Question 2

    23 Apr 2025 S1

    134
    The equation of motion of the particle is s=at2+bt+cs =at^{2}+ bt + c. If the displacement after 1 second is 20 m , velocity after 2 seconds is 30 m/30\text{ }m/ seconds and the acceleration is 10 m/10\text{ }m/ seconds  2\ ^{2}, then

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