The position of a particle between t = 0 and t = 2.00s is given by x(t)=(3.00m/s^3)t^3 - (1.00m/s^2)t^2+(9.00m/s)t. At what time(s) between t = 0 and t = 2.00 s is(are) the particle instantaneously at rest? At what time(s) between t =0 and t = 2.00 s is(are) the velocity of the particle instantaneously not changing? What is the particle’s greatest distance from the origin (x =0) between t = 0 and t = 2.00s? At what time(s) between t = 0 and t = 2.00s is(are) the particle speeding up at the greatest rate? At what time(s) between t = 0 and t = 2.00s is(are) the particle slowing down at the greatest rate?

The position of a particle between t = 0 and t = 2.00s is given by x(t)=(3.00m/s^3)t^3 - (1.00m/s^2)t^2+(9.00m/s)t. At what time(s) between t = 0 and t = 2.00 s is(are) the particle instantaneously at rest? At what time(s) between t =0 and t = 2.00 s is(are) the velocity of the particle instantaneously not changing? What is the particle’s greatest distance from the origin (x =0) between t = 0 and t = 2.00s? At what time(s) between t = 0 and t = 2.00s is(are) the particle speeding up at the greatest rate? At what time(s) between t = 0 and t = 2.00s is(are) the particle slowing down at the greatest rate?

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Question

The position of a particle between t = 0 and t = 2.00s is given by x(t)=(3.00m/s^3)t^3 - (1.00m/s^2)t^2+(9.00m/s)t.
At what time(s) between t = 0 and t = 2.00 s is(are) the particle instantaneously at rest?
At what time(s) between t =0 and t = 2.00 s is(are) the velocity of the particle instantaneously not changing?
What is the particle’s greatest distance from the origin (x =0) between t = 0 and t = 2.00s?

At what time(s) between t = 0 and t = 2.00s is(are) the particle speeding up at the greatest rate?
At what time(s) between t = 0 and t = 2.00s is(are) the particle slowing down at the greatest rate?

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