1. The position of a moving particle is given by the function

\( s(t)=2t^3-9t^2+12t \)

where \(s\) is in meters and \(t\) in seconds.

(a) Find the velocity and acceleration at any time \(t\).


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(b) Find the average velocity over the time interval \([1,3]\).


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(c) Find the velocity after 1 s? After 3 s?


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(d) Find the acceleration after 2 s?


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(e) When is the particle at rest?


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(f) When is the particle moving forward? Backwards?


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(g) Draw a diagram for the motion of this particle.


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(h) Find the total distance traveled during the first five seconds.


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(i) Find the displacement during the first five seconds.


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(j) When is the particle moving at constant speed?


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(k) When is the particle speeding up (accelerating)? Slowing down (deccelerating)?


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2. A rock is thrown vertically upwards on a planet. Its height after \(t\) seconds is,

\( h(t)=20 t- 2t^2\)

where \(h\) is in meters and \(t\) in seconds.


(a) Find the velocity of the rock after 6 seconds.


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(b) Find the maximum height reached by the rock.


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(c) Find the velocity of the rock when it hits the ground.


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(d) Find the velocity when the rock is 18 meters above the ground on the way up and on the way down.


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