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:

Flat Affect

Flat affect is a term used in psychology to describe a significant lack of emotional expressiveness or reaction in an individual, often seen in some mental health disorders.

Avolition

A lack of motivation or inability to initiate and persist in goal-directed activities.

Catatonic Stupor

A state of psychic and motor immobility and behavioral abnormality marked by periods of rigidity and excitement.

Heritability

A measure of how much of the variation in a trait within a population is due to genetic differences.