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calculus

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a particle moves along the x-axis in such a way that its acceleration at any time t is given by a(t)= 6t - 18. At time t = 0, the velocity v(t) = 24. and at time t = 1, the position x(t) = 20
i have to find the expression for the velocity and what values t is at rest

  • calculus - ,

    since a(t) = 6t -18
    v(t) = 3t^2 - 18 + c
    but we are told v(0) = 24
    so 24 = 0 + 0 + c, ----> c = 24

    if v(t) = 3t^2 - 18t + 24
    x(t) = t^3 - 9t^2 + 24t + k
    but we are told x(1) = 20
    so 20 = 1 - 9 + 24 + k , ---> k = 4

    x(t) = t^3 - 9t^2 + 24t + 4

    Your last sentence is confusing.
    Did you mean " ... and what values of t the particle is at rest" ?

    anyway, since you now have all 3 equations, I am pretty sure you can proceed from there

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