The Position Function for a Particle Moving Along the X-Axis $x ( t ) = t ^ { 4 } - 8 t ^ { 3 } + 6 t ^ { 2 } + 40 t - 20$

question 167

Essay

The position function for a particle moving along the x-axis at time t > 0 (in seconds) has its x-coordinate given by $x ( t ) = t ^ { 4 } - 8 t ^ { 3 } + 6 t ^ { 2 } + 40 t - 20$ .(a) Find a formula for the velocity and acceleration of the particle at any time t.(b) What is the velocity of the particle when t = 3? What does this value indicate?

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Definitions:

Combined Margin

A measure used in financial analysis that aggregates gross profit, operating margin, and net margin.

Fixed Expenses

Costs that do not change with the volume of production or sales, such as rent, salaries, and insurance.

Combined Turnover

A measure of a company’s ability to use its assets and liabilities effectively to generate sales, combining inventory turnover with accounts receivable turnover.

Fixed Expenses

Expenses that remain constant regardless of the amount of production or business operations, like lease payments or wages.