Question

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. *

Answer 1

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)=$6\sdot8-6=42$ $m/s^{2}$