A particle moves along the x-axis so that at time t\ge 0t≥0 its velocity is given by v(t)=6t^2-84t-90.v(t)=6t 2 −84t−90. Determine all intervals when the acceleration of the particle is negative.

Question

A particle moves along the x-axis so that at time t≥0 its velocity is given by v(t)=6t2−84t−90. Determine all intervals when the acceleration of the particle is negative.

Answer 1

Acceleration a(t) = v'(t) = 12t - 84 < 0; 12t < 84; t < 7. So on time interval [0,7) a(t) < 0.