Question #127879

The position of the particle that moves along the x-axis is given by x=t3-3t2-45t (m), where t is the time in seconds. Determine the position, velocity, and acceleration, and distance traveled at t=8 sec. *

Expert's answer

x(t)=x(8)= "8^{3}-3\\sdot8^{2}-45\\sdot8=-40" m

v(t)=x'(t)="3t^{2}-6t-45"

v(8)="3\\sdot8^2-6\\sdot8-45=99" m/s

a(t)=v'(t)=6t-6

a(8)="6\\sdot8-6=42" "m\/s^{2}"

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