Calculus

The position of a particle moving on a horizontal line is given by s(t)=2t^3-15t^2+24t-5, where s is measured in feet and t in seconds.
a: What is the initial position of the particle?
b: What is the average velocity of the particle on the interval [0,2]?Indicate units of measure
c: Find a formula for the instantaneous velocity of the particle.
d: When is the particle at rest?
e: When is the particle moving to the right? When is it moving to the left?
f: At t=2 seconds, is the particle moving away from the origin or towards the origin?
h: What is the average acceleration of the particle on the interval [0,2]?
i: Find a formula for the instantaneous acceleration of the particle.
j: At t=2 seconds, is the particle slowing down or speeding up?

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  1. a) sub in t = 0
    b) avg vel = (s(2) - s(0) )/(2-0) = ...
    c) s ' (t) = 6t^2 - 30t + 24

    d) particle is at rest, when velocity = 0 , that is ...
    6t^2 - 30t + 24 = 0
    t^2 - 5t +4 = 0
    (t-1)(t-4) = 0
    when t = 1 or when t = 4

    f) sub t=2 into the derivative of c)
    if it is positive, ---> to the right
    if it is negative, ---> to the left

    e) same steps as b) except use the velocity expression

    you do some of them.

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  2. How do you do E on this problem??

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