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Displacement by integrating velocity or acceleration given as a function of time

This type of question, asked 2 times: 2021 Paper 8, 2021 Paper 15. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 8

    9
    The velocity of a particle is v=v0+gt+Ft2v =v_{0}+ gt +Ft^{2}. Its position is x=0x = 0 at t=0t = 0; then its displacement after time (t=1)(t= 1) is:

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  2. Question 2

    2021 Paper 15

    3
    A particle starts from rest with acceleration a=αt+βt2a=\alpha t+\beta t^{2} where α\alpha and β\beta are constant. Find its displacement between t=1t = 1 and t=2t = 2 seconds.

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