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

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?