The Position of a Particle Is Given by the Function $2 t ^ { 3 } - 9 t ^ { 2 } + 12 t$

question 106

Essay

The position of a particle is given by the function s(t) = $2 t ^ { 3 } - 9 t ^ { 2 } + 12 t$ , where t is measured in seconds and s in meters.(a) Find the velocity at time t.(b) When is the particle at rest?
(c) When is the particle moving in the positive direction?
(d) Draw a diagram to represent the motion of the particle.(e) Find the total distance traveled by the particle during the time interval [1,3].

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Definitions:

Inventory Levels

The quantity of stock on hand at any given time, which companies manage to meet customer demand without incurring unnecessary costs or losses.

Carrying Cost

The total cost of holding inventory, including warehousing, spoilage, depreciation, and opportunity costs.

Economic Order Quantity

A calculation to determine the most cost-effective quantity of inventory to order, balancing ordering costs with holding costs.

Unit Variable

Costs that vary directly with the level of production or sales volume, such as materials and labor.