Will mark as BRAINLIEST-… The Displacement x of particle moving in one dimension under the action of constant force is relat

Question

Will mark as BRAINLIEST…….

The Displacement x of particle moving in one dimension under the action of constant force is related to the time by equation 4x³+3x²-5x+2 , where x is in meters and t is in sec.
a)Find velocity of particle at i) t=2 sec ii) t=4 sec.
b) Find the acceleration of the particle at t=3 sec.

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Kiệt Gia 4 years 2021-08-11T07:47:59+00:00 1 Answers 11 views 0

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  1. giabao
    0
    2021-08-11T07:49:48+00:00
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    Explanation:

    It is given that,

    The Displacement x of particle moving in one dimension under the action of constant force is related to the time by equation as:

    x=4t^3+3t^2-5t+2

    Where,

    x is in meters and t is in sec

    We know that,

    Velocity,

    v=\dfrac{dx}{dt}\\\\v=\dfrac{d(4t^3+3t^2-5t+2)}{dt}\\\\v=12t^2+6t-5

    (a) i. t = 2 s

    v=12(2)^2+6(2)-5=55\ m/s

    At t = 4 s

    v=12(4)^2+6(4)-5=211\ m/s

    (b) Acceleration,

    a=\dfrac{dv}{dt}\\\\a=\dfrac{d(12t^2+6t-5)}{dt}\\\\a=24t+6

    Pu t = 3 s in above equation

    So,

    a=24(3)+6\\\\a=78\ m/s^2

    Hence, (a) (i) v = 55 m/s (ii) v = 211 m/s and (b) 78 m/s²

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